Clase 12 Métodos basados en árboles: boosting
Boosting también utiliza la idea de un “ensamble” de árboles. La diferencia grande con bagging y bosques aleatorios en que la sucesión de árboles de boosting se ‘adapta’ al comportamiento del predictor a lo largo de las iteraciones, haciendo reponderaciones de los datos de entrenamiento para que el algoritmo se concentre en las predicciones más pobres. Boosting generalmente funciona bien con árboles chicos (cada uno con sesgo alto), mientras que bosques aleatorios funciona con árboles grandes (sesgo bajo).
En boosting usamos muchos árboles chicos adaptados secuencialmente. La disminución del sesgo proviene de usar distintos árboles que se encargan de adaptar el predictor a distintas partes del conjunto de entrenamiento. El control de varianza se logra con tasas de aprendizaje y tamaño de árboles, como veremos más adelante.
En bosques aleatorios usamos muchos árboles grandes, cada uno con una muestra de entrenamiento perturbada (bootstrap). El control de varianza se logra promediando sobre esas muestras bootstrap de entrenamiento.
Igual que bosques aleatorios, boosting es también un método que generalmente tiene alto poder predictivo.
12.1 Algoritmo FSAM (forward stagewise additive modeling)
Aunque existen versiones de boosting (Adaboost) desde los 90s, una buena manera de entender los algoritmos es mediante un proceso general de modelado por estapas (FSAM).
12.1.1 Discusión
Consideramos primero un problema de regresión, que queremos atacar con un predictor de la forma \[f(x) = \sum_{k=1}^m \beta_k b_k(x),\] donde los \(b_k\) son árboles. Podemos absorber el coeficiente \(\beta_k\) dentro del árbol \(b_k(x)\), y escribimos
\[f(x) = \sum_{k=1}^m T_k(x),\]
Para ajustar este tipo de modelos, buscamos minimizar la pérdida de entrenamiento:
\[\begin{equation} \min \sum_{i=1}^N L(y^{(i)}, \sum_{k=1}^M T_k(x^{(i)})) \end{equation}\]Este puede ser un problema difícil, dependiendo de la familia que usemos para los árboles \(T_k\), y sería difícil resolver por fuerza bruta. Para resolver este problema, podemos intentar una heurística secuencial o por etapas:
Si tenemos \[f_{m-1}(x) = \sum_{k=1}^{m-1} T_k(x),\]
intentamos resolver el problema (añadir un término adicional)
\[\begin{equation} \min_{T} \sum_{i=1}^N L(y^{(i)}, f_{m-1}(x^{(i)}) + T(x^{(i)})) \end{equation}\]Por ejemplo, para pérdida cuadrática (en regresión), buscamos resolver
\[\begin{equation} \min_{T} \sum_{i=1}^N (y^{(i)} - f_{m-1}(x^{(i)}) - T(x^{(i)}))^2 \end{equation}\] Si ponemos \[ r_{m-1}^{(i)} = y^{(i)} - f_{m-1}(x^{(i)}),\] que es el error para el caso \(i\) bajo el modelo \(f_{m-1}\), entonces reescribimos el problema anterior como \[\begin{equation} \min_{T} \sum_{i=1}^N ( r_{m-1}^{(i)} - T(x^{(i)}))^2 \end{equation}\]Este problema consiste en ajustar un árbol a los residuales o errores del paso anterior. Otra manera de decir esto es que añadimos un término adicional que intenta corregir los que el modelo anterior no pudo predecir bien. La idea es repetir este proceso para ir reduciendo los residuales, agregando un árbol a la vez.
La primera idea central de boosting es concentrarnos, en el siguiente paso, en los datos donde tengamos errores, e intentar corregir añadiendo un término adicional al modelo.
12.1.2 Algoritmo FSAM
Esta idea es la base del siguiente algoritmo:
Algoritmo FSAM (forward stagewise additive modeling)
- Tomamos \(f_0(x)=0\)
- Para \(m=1\) hasta \(M\),
- Resolvemos \[T_m = argmin_{T} \sum_{i=1}^N L(y^{(i)}, f_{m-1}(x^{(i)}) + T(x^{(i)}))\]
- Ponemos \[f_m(x) = f_{m-1}(x) + T_m(x)\]
- Nuestro predictor final es \(f(x) = \sum_{m=1}^M T_(x)\).
Observaciones: Generalmente los árboles sobre los que optimizamos están restringidos a una familia relativamente chica: por ejemplo, árboles de profundidad no mayor a \(2,3,\ldots, 8\).
Este algoritmo se puede aplicar directamente para problemas de regresión, como vimos en la discusión anterior: simplemente hay que ajustar árboles a los residuales del modelo del paso anterior. Sin embargo, no está claro cómo aplicarlo cuando la función de pérdida no es mínimos cuadrados (por ejemplo, regresión logística).
Ejemplo (regresión)
Podemos hacer FSAM directamente sobre un problema de regresión.
set.seed(227818)
library(rpart)
library(tidyverse)
x <- rnorm(200, 0, 30)
y <- 2*ifelse(x < 0, 0, sqrt(x)) + rnorm(200, 0, 0.5)
dat <- data.frame(x=x, y=y)Pondremos los árboles de cada paso en una lista. Podemos comenzar con una constante en lugar de 0.
arboles_fsam <- list()
arboles_fsam[[1]] <- rpart(y~x, data = dat,
control = list(maxdepth=0))
arboles_fsam[[1]]## n= 200
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 200 5370.398 4.675925 *Ahora construirmos nuestra función de predicción y el paso que agrega un árbol
predecir_arboles <- function(arboles_fsam, x){
preds <- lapply(arboles_fsam, function(arbol){
predict(arbol, data.frame(x=x))
})
reduce(preds, `+`)
}
agregar_arbol <- function(arboles_fsam, dat, plot=TRUE){
n <- length(arboles_fsam)
preds <- predecir_arboles(arboles_fsam, x=dat$x)
dat$res <- y - preds
arboles_fsam[[n+1]] <- rpart(res ~ x, data = dat,
control = list(maxdepth = 1))
dat$preds_nuevo <- predict(arboles_fsam[[n+1]])
dat$preds <- predecir_arboles(arboles_fsam, x=dat$x)
g_res <- ggplot(dat, aes(x = x)) + geom_line(aes(y=preds_nuevo)) +
geom_point(aes(y=res)) + labs(title = 'Residuales') + ylim(c(-10,10))
g_agregado <- ggplot(dat, aes(x=x)) + geom_line(aes(y=preds), col = 'red',
size=1.1) +
geom_point(aes(y=y)) + labs(title ='Ajuste')
if(plot){
print(g_res)
print(g_agregado)
}
arboles_fsam
}Ahora construiremos el primer árbol. Usaremos ‘troncos’ (stumps), árboles con un solo corte: Los primeros residuales son simplemente las \(y\)’s observadas
arboles_fsam <- agregar_arbol(arboles_fsam, dat)## Warning: Removed 8 rows containing missing values (geom_point).
Ajustamos un árbol de regresión a los residuales:
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
Después de 20 iteraciones obtenemos:
for(j in 1:19){
arboles_fsam <- agregar_arbol(arboles_fsam, dat, plot = FALSE)
}
arboles_fsam <- agregar_arbol(arboles_fsam, dat)
12.1.3 FSAM para clasificación binaria.
Para problemas de clasificación, no tiene mucho sentido trabajar con un modelo aditivo sobre las probabilidades:
\[p(x) = \sum_{k=1}^m T_k(x),\]
Así que hacemos lo mismo que en regresión logística. Ponemos
\[f(x) = \sum_{k=1}^m T_k(x),\]
y entonces las probabilidades son \[p(x) = h(f(x)),\]
donde \(h(z)=1/(1+e^{-z})\) es la función logística. La optimización de la etapa \(m\) según fsam es
\[\begin{equation} T = argmin_{T} \sum_{i=1}^N L(y^{(i)}, f_{m-1}(x^{(i)}) + T(x^{(i)})) \tag{12.1} \end{equation}\]y queremos usar la devianza como función de pérdida. Por razones de comparación (con nuestro libro de texto y con el algoritmo Adaboost que mencionaremos más adelante), escogemos usar \[y \in \{1,-1\}\]
en lugar de nuestro tradicional \(y \in \{1,0\}\). En ese caso, la devianza binomial se ve como
\[L(y, z) = -\left [ (y+1)\log h(z) - (y-1)\log(1-h(z))\right ],\] que a su vez se puede escribir como (demostrar):
\[L(y,z) = 2\log(1+e^{-yz})\] Ahora consideremos cómo se ve nuestro problema de optimización:
\[T = argmin_{T} 2\sum_{i=1}^N \log (1+ e^{-y^{(i)}(f_{m-1}(x^{(i)}) + T(x^{(i)})})\]
Nótese que sólo optimizamos con respecto a \(T\), así que podemos escribir
\[T = argmin_{T} 2\sum_{i=1}^N \log (1+ d_{m,i}e^{- y^{(i)}T(x^{(i)})})\]
Y vemos que el problema es más difícil que en regresión. No podemos usar un ajuste de árbol usual de regresión o clasificación, como hicimos en regresión. No está claro, por ejemplo, cuál debería ser el residual que tenemos que ajustar (aunque parece un problema donde los casos de entrenamiento están ponderados por \(d_{m,i}\)). Una solución para resolver aproximadamente este problema de minimización, es gradient boosting.
12.2 Gradient boosting
La idea de gradient boosting es replicar la idea del residual en regresión, y usar árboles de regresión para resolver (12.1).
Gradient boosting es una técnica general para funciones de pérdida generales.Regresamos entonces a nuestro problema original
\[(\beta_m, b_m) = argmin_{T} \sum_{i=1}^N L(y^{(i)}, f_{m-1}(x^{(i)}) + T(x^{(i)}))\]
La pregunta es: ¿hacia dónde tenemos qué mover la predicción de \(f_{m-1}(x^{(i)})\) sumando el término \(T(x^{(i)})\)? Consideremos un solo término de esta suma, y denotemos \(z_i = T(x^{(i)})\). Queremos agregar una cantidad \(z_i\) tal que el valor de la pérdida \[L(y, f_{m-1}(x^{(i)})+z_i)\] se reduzca. Entonces sabemos que podemos mover la z en la dirección opuesta al gradiente
\[z_i = -\gamma \frac{\partial L}{\partial z}(y^{(i)}, f_{m-1}(x^{(i)}))\]
Sin embargo, necesitamos que las \(z_i\) estén generadas por una función \(T(x)\) que se pueda evaluar en toda \(x\). Quisiéramos que \[T(x^{(i)})\approx -\gamma \frac{\partial L}{\partial z}(y^{(i)}, f_{m-1}(x^{(i)}))\] Para tener esta aproximación, podemos poner \[g_{i,m} = -\frac{\partial L}{\partial z}(y^{(i)}, f_{m-1}(x^{(i)}))\] e intentar resolver \[\begin{equation} \min_T (g_{i,m} - T(x^{(i)}))^2, \tag{12.2} \end{equation}\]es decir, intentamos replicar los gradientes lo más que sea posible. Este problema lo podemos resolver con un árbol usual de regresión. Finalmente, podríamos escoger \(\nu\) (tamaño de paso) suficientemente chica y ponemos \[f_m(x) = f_{m-1}(x)+\nu T(x).\]
Podemos hacer un refinamiento adicional que consiste en encontrar los cortes del árbol \(T\) según (12.2), pero optimizando por separado los valores que T(x) toma en cada una de las regiones encontradas.
12.2.1 Algoritmo
Gradient boosting (versión simple)
Inicializar con \(f_0(x) =\gamma\)
Para \(m=0,1,\ldots, M\),
Para \(i=1,\ldots, n\), calculamos el residual \[r_{i,m}=-\frac{\partial L}{\partial z}(y^{(i)}, f_{m-1}(x^{(i)}))\]
Ajustamos un árbol de regresión a la respuesta \(r_{1,m},r_{2,m},\ldots, r_{n,m}\). Supongamos que tiene regiones \(R_{j,m}\).
- Resolvemos (optimizamos directamente el valor que toma el árbol en cada región - este es un problema univariado, más fácil de resolver) \[\gamma_{j,m} = argmin_\gamma \sum_{x^{(i)}\in R_{j,m}} L(y^{(i)},f_{m-1}(x^{i})+\gamma )\] para cada región \(R_{j,m}\) del árbol del inciso anterior.
- Actualizamos \[f_m (x) = f_{m-1}(x) \sum_j \gamma_{j,m} I(x\in R_{j,m})\]
- El predictor final es \(f_M(x)\).
12.2.2 Funciones de pérdida
Para aplicar gradient boosting, tenemos primero que poder calcular el gradiente de la función de pérdida. Algunos ejemplos populares son:
- Pérdida cuadrática: \(L(y,f(x))=(y-f(x))^2\), \(\frac{\partial L}{\partial z} = -2(y-f(x))\).
- Pérdida absoluta (más robusta a atípicos que la cuadrática) \(L(y,f(x))=|y-f(x)|\), \(\frac{\partial L}{\partial z} = signo(y-f(x))\).
- Devianza binomial \(L(y, f(x))\) = -(1+e^{-yf(x)}), \(y\in\{-1,1\}\), \(\frac{\partial L}{\partial z} = I(y=1) - h(f(x))\).
- Adaboost, pérdida exponencial (para clasificación) \(L(y,z) = e^{-yf(x)}\), \(y\in\{-1,1\}\), \(\frac{\partial L}{\partial z} = -ye^{-yf(x)}\).
12.2.3 Discusión: adaboost (opcional)
Adaboost es uno de los algoritmos originales para boosting, y no es necesario usar gradient boosting para aplicarlo. La razón es que los árboles de clasificación \(T(x)\) toman valores \(T(x)\in \{-1,1\}\), y el paso de optimización (12.1) de cada árbol queda
\[T = argmin_{T} \sum_{i=1}^N e^{-y^{(i)}f_{m-1}(x^{(i)})} e^{-y^{(i)}T(x^{(i)})} \] \[T = argmin_{T} \sum_{i=1}^N d_{m,i} e^{-y^{(i)}T(x^{(i)})} \] De modo que la función objetivo toma dos valores: Si \(T(x^{i})\) clasifica correctamente, entonces \(e^{-y^{(i)}T(x^{(i)})}=e^{-1}\), y si clasifica incorrectamente \(e^{-y^{(i)}T(x^{(i)})}=e^{1}\). Podemos entonces encontrar el árbol \(T\) construyendo un árbol usual pero con datos ponderados por \(d_{m,i}\), donde buscamos maximizar la tasa de clasificación correcta (puedes ver más en nuestro libro de texto, o en (Hastie, Tibshirani, and Friedman 2017).
¿Cuáles son las consecuencias de usar la pérdida exponencial? Una es que perdemos la conexión con los modelos logísticos e interpretación de probabilidad que tenemos cuando usamos la devianza. Sin embargo, son similares: compara cómo se ve la devianza (como la formulamos arriba, con \(y\in\{-1,1\}\)) con la pérdida exponencial.
Ejemplo
Podemos usar el paquete de R gbm para hacer gradient boosting. Para el caso de precios de casas de la sección anterior (un problema de regresión).
Fijaremos el número de árboles en 50, de profundidad 3, usando 75% de la muestra para entrenar y el restante para validación:
library(gbm)## Loading required package: survival## Loading required package: lattice## Loading required package: splines## Loading required package: parallel## Loaded gbm 2.1.3entrena <- read_rds('datos/ameshousing-entrena-procesado.rds')
set.seed(23411)
ajustar_boost <- function(entrena, ...){
mod_boosting <- gbm(log(vSalePrice) ~., data = entrena,
distribution = 'gaussian',
n.trees = 200,
interaction.depth = 3,
shrinkage = 1, # tasa de aprendizaje
bag.fraction = 1,
train.fraction = 0.75)
mod_boosting
}
house_boosting <- ajustar_boost(entrena)
dat_entrenamiento <- data_frame(entrena = sqrt(house_boosting$train.error),
valida = sqrt(house_boosting$valid.error),
n_arbol = 1:length(house_boosting$train.error)) %>%
gather(tipo, valor, -n_arbol)
print(house_boosting)## gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian",
## data = entrena, n.trees = 200, interaction.depth = 3, shrinkage = 1,
## bag.fraction = 1, train.fraction = 0.75)
## A gradient boosted model with gaussian loss function.
## 200 iterations were performed.
## The best test-set iteration was 20.
## There were 79 predictors of which 28 had non-zero influence.ggplot(dat_entrenamiento, aes(x=n_arbol, y=valor, colour=tipo, group=tipo)) +
geom_line()
Que se puede graficar también así:
gbm.perf(house_boosting)## Using test method...
## [1] 20Como vemos, tenemos que afinar los parámetros del algoritmo.
12.3 Modificaciones de Gradient Boosting
Hay algunas adiciones al algoritmo de gradient boosting que podemos usar para mejorar el desempeño:
12.3.1 Tasa de aprendizaje (shrinkage)
Funciona bien modificar el algoritmo usando una tasa de aprendizae \(0<\nu<1\): \[f_m(x) = f_{m-1}(x) + \nu \sum_j \gamma_{j,m} I(x\in R_{j,m})\]
Este parámetro sirve como una manera de evitar sobreajuste rápido cuando construimos los predictores. Si este número es muy alto, podemos sobreajustar rápidamente con pocos árboles, y terminar con predictor de varianza alta. Si este número es muy bajo, puede ser que necesitemos demasiadas iteraciones para llegar a buen desempeño.
Igualmente se prueba con varios valores de \(0<nu<1\) (típicamente \(\nu<0.1\)) para mejorar el desempeño en validación. Nota: cuando hacemos \(\nu\) más chica, es necesario hacer \(M\) más grande (correr más árboles) para obtener desempeño óptimo.
Veamos que efecto tiene en nuestro ejemplo:
modelos_dat <- data_frame(n_modelo = 1:4, shrinkage = c(0.05, 0.1, 0.5, 1))
modelos_dat <- modelos_dat %>%
mutate(modelo = map(shrinkage, boost)) %>%
mutate(eval = map(modelo, eval_modelo))
modelos_dat## # A tibble: 4 x 4
## n_modelo shrinkage modelo eval
## <int> <dbl> <list> <list>
## 1 1 0.05 <S3: gbm> <tibble [1,000 x 3]>
## 2 2 0.10 <S3: gbm> <tibble [1,000 x 3]>
## 3 3 0.50 <S3: gbm> <tibble [1,000 x 3]>
## 4 4 1.00 <S3: gbm> <tibble [1,000 x 3]>graf_eval <- modelos_dat %>% select(shrinkage, eval) %>% unnest
graf_eval## # A tibble: 4,000 x 4
## shrinkage n_arbol tipo valor
## <dbl> <int> <chr> <dbl>
## 1 0.05 1 entrena 0.3914774
## 2 0.05 2 entrena 0.3795092
## 3 0.05 3 entrena 0.3683144
## 4 0.05 4 entrena 0.3578551
## 5 0.05 5 entrena 0.3480027
## 6 0.05 6 entrena 0.3387286
## 7 0.05 7 entrena 0.3300476
## 8 0.05 8 entrena 0.3210405
## 9 0.05 9 entrena 0.3127008
## 10 0.05 10 entrena 0.3047083
## # ... with 3,990 more rowsggplot(filter(graf_eval, tipo=='valida'), aes(x = n_arbol, y= valor, colour=factor(shrinkage), group =
shrinkage)) + geom_line() +
facet_wrap(~tipo)
Obsérvese que podemos obtener un mejor resultado de validación afinando la tasa de aprendizaje. Cuando es muy grande, el modelo rápidamente sobreajusta cuando agregamos árboles. Si la tasa es demasiado chica, podos tardar mucho en llegar a un predictor de buen desempeño.
¿Cómo crees que se ven las gráfica de error de entrenamiento?
12.3.2 Submuestreo (bag.fraction)
Funciona bien construir cada uno de los árboles con submuestras de la muestra de entrenamiento, como una manera adicional de reducir varianza al construir nuestro predictor (esta idea es parecida a la de los bosques aleatorios, aquí igualmente perturbamos la muestra de entrenamiento en cada paso para evitar sobreajuste). Adicionalmente, este proceso acelera considerablemente las iteraciones de boosting, y en algunos casos sin penalización en desempeño.
En boosting generalmente se toman submuestras (una fracción de alrededor de 0.5 de la muestra de entrenamiento, pero puede ser más chica para conjuntos grandes de entrenamiento) sin reemplazo.
Este parámetro también puede ser afinado con muestra de validación o validación cruzada.
boost <- ajustar_boost(entrena)
modelos_dat <- data_frame(n_modelo = 1:3,
bag.fraction = c(0.25, 0.5, 1),
shrinkage = 0.25)
modelos_dat <- modelos_dat %>%
mutate(modelo = pmap(., boost)) %>%
mutate(eval = map(modelo, eval_modelo))
modelos_dat## # A tibble: 3 x 5
## n_modelo bag.fraction shrinkage modelo eval
## <int> <dbl> <dbl> <list> <list>
## 1 1 0.25 0.25 <S3: gbm> <tibble [1,000 x 3]>
## 2 2 0.50 0.25 <S3: gbm> <tibble [1,000 x 3]>
## 3 3 1.00 0.25 <S3: gbm> <tibble [1,000 x 3]>graf_eval <- modelos_dat %>% select(bag.fraction, eval) %>% unnest
graf_eval## # A tibble: 3,000 x 4
## bag.fraction n_arbol tipo valor
## <dbl> <int> <chr> <dbl>
## 1 0.25 1 entrena 0.3404206
## 2 0.25 2 entrena 0.2948882
## 3 0.25 3 entrena 0.2582633
## 4 0.25 4 entrena 0.2316890
## 5 0.25 5 entrena 0.2106434
## 6 0.25 6 entrena 0.1946327
## 7 0.25 7 entrena 0.1825413
## 8 0.25 8 entrena 0.1733467
## 9 0.25 9 entrena 0.1652359
## 10 0.25 10 entrena 0.1596591
## # ... with 2,990 more rowsggplot((graf_eval), aes(x = n_arbol, y= valor, colour=factor(bag.fraction), group =
bag.fraction)) + geom_line() +
facet_wrap(~tipo)
En este ejemplo, podemos reducir el tiempo de ajuste usando una fracción de submuestro de 0.5, sin diferencias grandes en desempeño.
Ahora veamos los dos parámetros actuando en conjunto:
modelos_dat <- list(bag.fraction = c(0.1, 0.25, 0.5, 1),
shrinkage = c(0.01, 0.1, 0.25, 0.5)) %>% expand.grid
modelos_dat <- modelos_dat %>%
mutate(modelo = pmap(., boost)) %>%
mutate(eval = map(modelo, eval_modelo))
head(modelos_dat)## bag.fraction shrinkage
## 1 0.10 0.01
## 2 0.25 0.01
## 3 0.50 0.01
## 4 1.00 0.01
## 5 0.10 0.10
## 6 0.25 0.10
## modelo
## 1 12.02513, 12.22414, 12.17763, 12.28275, 12.2008, 12.6946, 11.93185, 12.56725, 12.27169, 11.8584, 11.69195, 11.76616, 12.77416, 11.75057, 12.30066, 11.90215, 11.78949, 11.86074, 11.59924, 11.97879, 11.79269, 12.75496, 11.67145, 12.38632, 11.75341, 11.84112, 12.56923, 11.80756, 12.6627, 12.10428, 11.23612, 11.37521, 11.85301, 12.19255, 12.03646, 12.50724, 12.70114, 11.96082, 11.94875, 11.79317, 11.35427, 11.88343, 12.03966, 11.8598, 11.81977, 11.83776, 12.57099, 12.4175, 12.49609, 11.54726, 11.75249, 12.06317, 11.68664, 11.51113, 12.81527, 11.77618, 11.95977, 12.23366, 12.22673, 12.81439, 11.75192, 12.03963, 11.47663, 12.2781, 11.86682, 12.35401, 12.70681, 12.38447, 12.23551, 11.31747, 12.40077, 12.43471, 11.70779, 12.16123, 11.8581, 11.62625, 11.44862, 11.69032, 11.72219, 11.74483, 11.60586, 12.13777, 12.01302, 12.46511, 11.74933, 12.02863, 12.59776, 12.08069, 11.93001, 11.51909, 11.78087, 11.54173, 11.7905, 11.8555, 11.99044, 12.18408, 12.04265, 12.28654, 11.65955, 11.27742, 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Min2, Mod, Otros, Typ, Fa, no-disponible, Otros, TA, Fin, no-disponible, RFn, Unf, Fa, Gd, no-disponible, Otros, TA, Attchd, Basment, BuiltIn, Detchd, no-disponible, Otros, GasA, GasW, Otros, Ex, Fa, Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 8, 0, 0, 0, 0, 218.6, 383.5, 525.6, 655, 806.4, 1065.5, 5644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117.2, 1474, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 74.9, 172, 280, 374.6, 477.5, 604.4, 736, 896, 1232, 2336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 552, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 0, 240, 295.6, 384, 440, 480, 516, 560, 620.2, 757.1, 1418, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 0, 1928, 1954, 1962, 1970, 1977, 1990, 1998, 2003, 2006, 2010, 334, 912, 1066.6, 1208, 1339, 1464, 1578, 1709.3, 1869, 2158.3, 5642, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1300, 5000, 7078.4, 8063.7, 8793.4, 9478.5, 10198.2, 11066.5, 12205.8, 14381.7, 215245, 0, 0, 24, 50, 60, 63, 70, 75, 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1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 5, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 3, 6, 3, 6, 6, 5, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 5, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 3, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 4, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 1, 6, 6, 6, 2, 3, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6, 1, 6, 6, 6, 1, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 5, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 5, 6, 6, 6, 4, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 5, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 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772, 786, 787, 795, 812, 815, 818, 819, 832, 835, 855, 861, 862, 869, 871, 878, 898, 905, 910, 939, 949, 959, 960, 964, 972, 987, 999, 1011, 1026, 1049, 1053, 1060, 1065, 1081, 1085, 1086, 1094, NA, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
## 2 12.02513, 12.2233, 12.09869, 12.27953, 12.12537, 12.61158, 11.91485, 12.53514, 12.2659, 11.83022, 11.75204, 11.7792, 12.76494, 11.76216, 12.28815, 11.92458, 11.81573, 11.88447, 11.63784, 11.92746, 11.73964, 12.68143, 11.72971, 12.39091, 11.74932, 11.86114, 12.50793, 11.80199, 12.62174, 12.09425, 11.16604, 11.26702, 11.84402, 12.18931, 12.03532, 12.54618, 12.67174, 11.92371, 11.96007, 11.77237, 11.34698, 11.88175, 12.02371, 11.89203, 11.80331, 11.8333, 12.59999, 12.41449, 12.44608, 11.59376, 11.77739, 12.05274, 11.70646, 11.49918, 12.78564, 11.76372, 11.99711, 12.25026, 12.21925, 12.875, 11.75164, 11.97973, 11.40491, 12.27701, 11.89198, 12.33468, 12.65017, 12.36213, 12.24696, 11.40576, 12.38501, 12.38443, 11.76083, 12.17727, 11.86609, 11.63479, 11.4418, 11.71194, 11.71135, 11.76615, 11.62467, 12.12436, 12.00613, 12.43319, 11.77216, 12.08099, 12.57857, 12.08159, 11.94032, 11.37052, 11.79105, 11.56295, 11.68992, 11.86675, 11.9834, 12.15526, 12.06975, 12.27359, 11.68949, 11.27195, 11.74157, 12.19677, 12.0814, 11.76122, 12.16016, 11.96431, 12.478, 11.45585, 11.54167, 11.60973, 12.19779, 11.85376, 12.08384, 12.62055, 12.28263, 12.25522, 12.0039, 11.77888, 11.81379, 12.60992, 12.03862, 12.03432, 11.46361, 11.84248, 12.00002, 12.07348, 11.33334, 11.85648, 11.41111, 11.84367, 11.79978, 12.22037, 12.2272, 11.90522, 12.25156, 12.01779, 12.14718, 11.88711, 12.225, 12.40745, 12.15402, 11.64668, 12.39412, 11.74114, 12.25366, 11.89208, 11.86725, 11.5643, 12.28579, 11.98655, 11.58109, 11.85505, 12.70594, 12.11593, 12.11724, 11.58549, 11.35393, 11.60458, 12.50126, 12.39653, 12.50873, 12.04192, 12.90823, 12.41324, 11.45234, 11.86288, 11.67583, 12.23187, 12.74921, 12.19898, 12.39821, 11.73365, 12.08856, 12.30086, 11.93318, 12.23503, 12.16936, 12.2859, 11.99713, 12.94993, 11.58094, 12.04368, 12.12683, 11.72114, 12.17079, 11.7035, 12.60174, 12.07104, 11.73545, 11.86684, 12.50649, 12.58769, 12.05506, 12.21214, 11.9882, 11.77431, 11.88792, 12.54996, 12.42792, 11.68746, 12.62587, 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Stucco, VinylSd, Wd Sdng, WdShing, AsbShng, BrkFace, CmentBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, Wd Shng, Ex, Fa, Gd, TA, GdPrv, GdWo, MnPrv, MnWw, no-disponible, Ex, Fa, Gd, no-disponible, Po, TA, BrkTil, CBlock, Otros, PConc, Slab, Maj1, Min1, Min2, Mod, Otros, Typ, Fa, no-disponible, Otros, TA, Fin, no-disponible, RFn, Unf, Fa, Gd, no-disponible, Otros, TA, Attchd, Basment, BuiltIn, Detchd, no-disponible, Otros, GasA, GasW, Otros, Ex, Fa, Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 8, 0, 0, 0, 0, 218.6, 383.5, 525.6, 655, 806.4, 1065.5, 5644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117.2, 1474, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 74.9, 172, 280, 374.6, 477.5, 604.4, 736, 896, 1232, 2336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 552, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 0, 240, 295.6, 384, 440, 480, 516, 560, 620.2, 757.1, 1418, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 0, 1928, 1954, 1962, 1970, 1977, 1990, 1998, 2003, 2006, 2010, 334, 912, 1066.6, 1208, 1339, 1464, 1578, 1709.3, 1869, 2158.3, 5642, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1300, 5000, 7078.4, 8063.7, 8793.4, 9478.5, 10198.2, 11066.5, 12205.8, 14381.7, 215245, 0, 0, 24, 50, 60, 63, 70, 75, 80, 92, 313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 16, 116, 205.2, 335, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15500, 1, 3, 4, 5, 6, 6, 7, 7, 8, 10, 12, 0, 0, 0, 0, 0, 25, 40, 57, 83.2, 130, 547, 1, 5, 5, 5, 5, 5, 5, 6, 7, 7, 9, 1, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 738, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 636.9, 755.8, 840, 910, 991.5, 1088, 1216, 1391.2, 1602.2, 6110, 2, 5, 5, 6, 6, 6, 7, 7, 8, 9, 14, 0, 0, 0, 0, 0, 0, 100, 144, 192, 262, 857, 1872, 1924.9, 1947.8, 1958, 1965, 1973, 1984, 1997.3, 2003, 2006, 2010, 1950, 1950, 1961.8, 1971, 1980, 1994, 1998, 2002, 2005, 2006, 2010, 2006, 2006, 2006, 2007, 2007, 2008, 2008, 2009, 2009, 2010, 2010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, vAlley, vBldgType, vBsmtCond, vBsmtExposure, vBsmtFinType1, vBsmtFinType2, vBsmtQual, vCentralAir, vCondition1, vCondition2, vElectrical, vExterCond, vExterior1st, vExterior2nd, vExterQual, vFence, vFireplaceQu, vFoundation, vFunctional, vGarageCond, vGarageFinish, vGarageQual, vGarageType, vHeating, vHeatingQC, vHouseStyle, vKitchenQual, vLandContour, vLandSlope, vLotConfig, vLotShape, vMasVnrType, vMiscFeature, vMSSubClass, vMSZoning, vNeighborhood, vPavedDrive, vPoolQC, vRoofMatl, vRoofStyle, vSaleCondition, vSaleType, vStreet, vId1, v1stFlrSF, v2ndFlrSF, v3SsnPorch, vBedroomAbvGr, vBsmtFinSF1, vBsmtFinSF2, vBsmtFullBath, vBsmtHalfBath, vBsmtUnfSF, vEnclosedPorch, vFireplaces, vFullBath, vGarageArea, vGarageCars, vGarageYrBlt, vGrLivArea, vHalfBath, vKitchenAbvGr, vLotArea, 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0, 1, 6, 6, 2, 6, 5, 5, 0, 0, 2, 6, 6, 1, 6, 1, 2, 1, 6, 1, 6, 0, 4, 2, 6, 2, 6, 5, 6, 2, 0, 2, 0, 0, 0, 3, 6, 6, 1, 2, 3, 6, 0, 1, 6, 3, 2, 1, 4, 1, 0, 4, 2, 1, 0, 1, 6, 6, 2, 5, 2, 5, 1, 6, 5, 0, 5, 1, 2, 6, 1, 0, 1, 0, 2, 0, 2, 3, 1, 0, 6, 1, 6, 6, 2, 1, 6, 2, 2, 6, 2, 2, 2, 6, 5, 0, 2, 6, 2, 3, 0, 2, 6, 0, 0, 1, 2, 0, 2, 5, 0, 5, 2, 0, 1, 0, 0, 6, 2, 6, 5, 0, 6, 0, 6, 2, 6, 6, 6, 2, 6, 2, 3, 5, 0, 2, 6, 6, 4, 0, 6, 2, 3, 6, 2, 1, 1, 6, 2, 0, 5, 6, 6, 2, 4, 6, 2, 6, 2, 2, 3, 1, 6, 6, 6, 4, 6, 0, 1, 2, 2, 2, 6, 2, 2, 2, 3, 2, 0, 3, 5, 2, 5, 1, 6, 2, 2, 2, 6, 4, 2, 6, 6, 2, 5, 2, 0, 2, 0, 4, 2, 2, 4, 4, 6, 6, 5, 5, 2, 0, 2, 2, 2, 5, 2, 6, 6, 1, 1, 2, 6, 2, 0, 0, 1, 5, 6, 1, 6, 1, 0, 1, 2, 2, 0, 0, 6, 1, 0, 2, 1, 6, 6, 2, 4, 1, 5, 2, 1, 2, 6, 6, 1, 0, 5, 1, 5, 0, 6, 2, 2, 6, 6, 2, 2, 0, 2, 1, 5, 2, 2, 1, 6, 3, 6, 2, 6, 6, 6, 6, 6, 2, 6, 2, 1, 1, 6, 2, 6, 6, 1, 6, 0, 1, 0, 0, 2, 2, 1, 6, 2, 5, 6, 0, 6, 1, 0, 0, 0, 0, 0, 2, 6, 0, 0, 1, 1, 2, 0, 6, 6, 2, 5, 2, 0, 0, 6, 5, 5, 2, 0, 5, 6, 4, 3, 2, 2, 5, 5, 1, 1, 2, 6, 6, 1, 6, 6, 2, 0, 6, 6, 6, 6, 5, 6, 6, 6, 6, 0, 0, 5, 2, 5, 2, 6, 2, 5, 2, 1, 5, 4, 2, 4, 6, 5, 1, 5, 3, 2, 2, 6, 0, 2, 0, 2, 0, 4, 5, 6, 6, 6, 6, 6, 2, 2, 6, 2, 2, 6, 6, 6, 2, 5, 1, 0, 6, 1, 3, 6, 3, 2, 6, 2, 0, 6, 5, 6, 6, 2, 2, 6, 6, 5, 1, 2, 6, 1, 0, 6, 5, 1, 0, 2, 6, 2, 0, 3, 6, 6, 6, 0, 5, 2, 6, 2, 0, 6, 2, 5, 1, 0, 2, 2, 3, 2, 1, 2, 6, 6, 2, 6, 0, 2, 2, 2, 2, 2, 6, 5, 0, 6, 6, 6, 0, 0, 4, 2, 3, 6, 6, 5, 0, 3, 6, 6, 0, 0, 6, 3, 0, 6, 6, 2, 5, 6, 2, 6, 6, 6, 0, 1, 2, 2, 3, 3, 5, 6, 2, 2, 6, 5, 2, 2, 2, 6, 0, 6, 6, 6, 2, 2, 0, 2, 1, 0, 1, 2, 2, 6, 6, 5, 3, 1, 6, 5, 1, 6, 6, 5, 1, 1, 5, 2, 0, 2, 6, 0, 6, 2, 6, 1, 6, 5, 1, 6, 2, 6, 2, 6, 2, 2, 0, 6, 6, 2, 1, 4, 2, 6, 0, 6, 2, 1, 5, 0, 0, 2, 6, 0, 6, 2, 1, 1, 1, 6, 3, 6, 6, 0, 6, 0, 2, 2, 2, 6, 2, 2, 6, 6, 3, 5, 2, 6, 2, 6, 6, 2, 6, 2, 6, 0, 2, 2, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 0, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 3, 1, 1, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 5, 3, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 1, 6, 6, 6, 6, 6, 5, 5, 3, 6, 6, 1, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 4, 0, 6, 6, 0, 6, 3, 6, 6, 5, 6, 6, 2, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 1, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 1, 6, 6, 5, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 5, 6, 4, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 5, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 3, 6, 3, 6, 6, 5, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 5, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 3, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 4, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 1, 6, 6, 6, 2, 3, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6, 1, 6, 6, 6, 1, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 5, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 5, 6, 6, 6, 4, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 5, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 3, 4, 6, 4, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 0, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 2, 5, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 3, 2, 2, 2, 4, 2, 2, 0, 2, 4, 4, 4, 0, 4, 2, 4, 4, 4, 3, 4, 4, 0, 4, 2, 2, 4, 2, 4, 0, 4, 4, 4, 4, 0, 4, 0, 0, 2, 4, 4, 3, 4, 4, 2, 2, 4, 0, 0, 2, 4, 4, 2, 4, 2, 0, 4, 4, 2, 2, 0, 4, 2, 4, 2, 4, 2, 0, 2, 2, 4, 4, 2, 4, 2, 4, 1, 2, 4, 4, 4, 4, 2, 0, 2, 4, 2, 2, 2, 2, 4, 2, 3, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 2, 3, 2, 4, 0, 1, 4, 4, 2, 4, 2, 0, 2, 4, 2, 4, 2, 2, 2, 4, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 2, 4, 0, 4, 4, 4, 4, 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 0, 4, 2, 4, 4, 3, 0, 2, 2, 2, 0, 2, 4, 4, 4, 4, 0, 2, 2, 4, 4, 2, 4, 2, 4, 2, 4, 0, 4, 2, 1, 3, 2, 1, 4, 2, 1, 2, 0, 2, 4, 2, 2, 4, 2, 0, 4, 4, 0, 2, 4, 1, 2, 4, 2, 4, 4, 2, 2, 4, 2, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 2, 4, 0, 4, 2, 4, 4, 2, 4, 2, 4, 4, 2, 4, 2, 2, 0, 4, 2, 4, 4, 2, 2, 2, 1, 4, 2, 2, 4, 2, 2, 2, 4, 2, 2, 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566, 570, 575, 578, 579, 583, 586, 589, 590, 592, 594, 599, 604, 617, 619, 620, 621, 629, 638, 640, 646, 647, 650, 653, 654, 656, 657, 663, 667, 674, 682, 690, 699, 709, 710, 712, 717, 718, 723, 732, 741, 744, 745, 758, 765, 767, 784, 788, 794, 797, 800, 802, 805, 811, 817, 820, 825, 826, 830, 834, 837, 838, 839, 840, 841, 842, 844, 848, 856, 864, 872, 885, 887, 893, 895, 919, 921, 923, 925, 927, 934, 953, 961, 967, 973, 980, 982, 983, 985, 1002, 1005, 1010, 1020, 1023, 1024, 1027, 1037, 1041, 1043, 1047, 1055, 1061, 1067, 1080, 1091, 1092, 5, 7, 19, 25, 36, 37, 46, 48, 56, 64, 72, 75, 79, 80, 84, 86, 87, 88, 92, 95, 102, 116, 124, 131, 133, 139, 143, 146, 166, 178, 186, 187, 188, 192, 195, 198, 199, 204, 205, 212, 221, 223, 224, 225, 229, 231, 243, 257, 260, 273, 275, 282, 283, 292, 294, 299, 308, 311, 313, 315, 316, 318, 319, 328, 329, 332, 339, 341, 347, 356, 362, 363, 365, 366, 373, 375, 379, 383, 387, 391, 396, 399, 405, 410, 421, 425, 426, 429, 435, 437, 439, 440, 445, 453, 459, 460, 461, 462, 464, 478, 482, 485, 489, 494, 495, 498, 504, 505, 507, 509, 510, 515, 516, 517, 519, 540, 542, 549, 552, 553, 568, 572, 576, 581, 584, 587, 588, 591, 593, 605, 606, 610, 612, 622, 632, 636, 637, 642, 644, 651, 652, 659, 661, 662, 670, 671, 675, 677, 678, 681, 694, 707, 715, 722, 724, 725, 726, 727, 728, 729, 733, 738, 739, 743, 746, 747, 749, 754, 755, 756, 760, 761, 763, 770, 775, 782, 783, 785, 790, 798, 803, 807, 809, 821, 823, 827, 828, 833, 846, 847, 853, 857, 858, 863, 865, 870, 873, 874, 877, 879, 882, 884, 889, 891, 894, 897, 901, 909, 911, 914, 917, 928, 930, 931, 933, 936, 937, 941, 944, 945, 952, 956, 963, 966, 968, 971, 974, 979, 981, 984, 991, 994, 997, 1000, 1004, 1007, 1008, 1013, 1015, 1016, 1017, 1031, 1035, 1036, 1038, 1039, 1042, 1044, 1045, 1048, 1057, 1058, 1064, 1066, 1071, 1073, 1087, 1090, 16, 24, 26, 27, 33, 38, 45, 52, 63, 66, 68, 73, 74, 78, 98, 99, 100, 101, 103, 109, 111, 118, 140, 142, 147, 157, 158, 162, 171, 200, 211, 214, 228, 230, 233, 234, 236, 237, 239, 240, 244, 250, 254, 263, 272, 276, 277, 288, 324, 340, 344, 353, 368, 369, 372, 378, 380, 385, 395, 412, 413, 419, 446, 470, 503, 532, 539, 560, 565, 567, 603, 614, 615, 625, 627, 634, 648, 655, 658, 680, 684, 698, 703, 704, 705, 711, 714, 721, 730, 748, 750, 757, 762, 766, 769, 772, 786, 787, 795, 812, 815, 818, 819, 832, 835, 855, 861, 862, 869, 871, 878, 898, 905, 910, 939, 949, 959, 960, 964, 972, 987, 999, 1011, 1026, 1049, 1053, 1060, 1065, 1081, 1085, 1086, 1094, NA, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
## 3 12.02513, 12.22757, 12.08995, 12.26471, 12.17461, 12.62188, 11.91387, 12.55632, 12.30478, 11.91426, 11.73557, 11.7875, 12.79045, 11.77404, 12.27486, 11.92284, 11.85218, 11.87141, 11.63826, 11.96938, 11.7639, 12.70662, 11.75551, 12.4056, 11.75191, 11.85538, 12.50005, 11.79239, 12.64052, 12.08067, 11.12989, 11.22216, 11.85237, 12.17838, 12.04697, 12.5471, 12.6974, 11.91558, 11.95289, 11.79527, 11.36168, 11.8895, 12.02203, 11.88105, 11.81181, 11.85657, 12.59098, 12.39373, 12.45031, 11.62229, 11.7641, 12.04634, 11.70794, 11.53389, 12.78199, 11.79809, 11.9868, 12.24323, 12.20398, 12.87842, 11.76511, 12.0168, 11.44044, 12.26254, 11.92381, 12.32919, 12.66334, 12.35166, 12.23702, 11.36035, 12.37589, 12.35915, 11.73899, 12.18462, 11.86269, 11.61844, 11.48173, 11.70795, 11.70465, 11.77179, 11.6172, 12.09516, 12.0022, 12.44464, 11.76903, 12.08287, 12.58115, 12.08053, 11.91807, 11.35027, 11.79609, 11.56511, 11.69882, 11.87831, 11.96864, 12.13651, 12.06272, 12.27751, 11.66383, 11.30941, 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AsbShng, BrkFace, CmentBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, Wd Shng, Ex, Fa, Gd, TA, GdPrv, GdWo, MnPrv, MnWw, no-disponible, Ex, Fa, Gd, no-disponible, Po, TA, BrkTil, CBlock, Otros, PConc, Slab, Maj1, Min1, Min2, Mod, Otros, Typ, Fa, no-disponible, Otros, TA, Fin, no-disponible, RFn, Unf, Fa, Gd, no-disponible, Otros, TA, Attchd, Basment, BuiltIn, Detchd, no-disponible, Otros, GasA, GasW, Otros, Ex, Fa, Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 8, 0, 0, 0, 0, 218.6, 383.5, 525.6, 655, 806.4, 1065.5, 5644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117.2, 1474, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 74.9, 172, 280, 374.6, 477.5, 604.4, 736, 896, 1232, 2336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 552, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 0, 240, 295.6, 384, 440, 480, 516, 560, 620.2, 757.1, 1418, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 0, 1928, 1954, 1962, 1970, 1977, 1990, 1998, 2003, 2006, 2010, 334, 912, 1066.6, 1208, 1339, 1464, 1578, 1709.3, 1869, 2158.3, 5642, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1300, 5000, 7078.4, 8063.7, 8793.4, 9478.5, 10198.2, 11066.5, 12205.8, 14381.7, 215245, 0, 0, 24, 50, 60, 63, 70, 75, 80, 92, 313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 16, 116, 205.2, 335, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15500, 1, 3, 4, 5, 6, 6, 7, 7, 8, 10, 12, 0, 0, 0, 0, 0, 25, 40, 57, 83.2, 130, 547, 1, 5, 5, 5, 5, 5, 5, 6, 7, 7, 9, 1, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 738, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 636.9, 755.8, 840, 910, 991.5, 1088, 1216, 1391.2, 1602.2, 6110, 2, 5, 5, 6, 6, 6, 7, 7, 8, 9, 14, 0, 0, 0, 0, 0, 0, 100, 144, 192, 262, 857, 1872, 1924.9, 1947.8, 1958, 1965, 1973, 1984, 1997.3, 2003, 2006, 2010, 1950, 1950, 1961.8, 1971, 1980, 1994, 1998, 2002, 2005, 2006, 2010, 2006, 2006, 2006, 2007, 2007, 2008, 2008, 2009, 2009, 2010, 2010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, vAlley, vBldgType, vBsmtCond, vBsmtExposure, vBsmtFinType1, vBsmtFinType2, vBsmtQual, vCentralAir, vCondition1, vCondition2, vElectrical, vExterCond, vExterior1st, vExterior2nd, vExterQual, vFence, vFireplaceQu, vFoundation, vFunctional, vGarageCond, vGarageFinish, vGarageQual, vGarageType, vHeating, vHeatingQC, vHouseStyle, vKitchenQual, vLandContour, vLandSlope, vLotConfig, vLotShape, vMasVnrType, vMiscFeature, vMSSubClass, vMSZoning, vNeighborhood, vPavedDrive, vPoolQC, vRoofMatl, vRoofStyle, vSaleCondition, vSaleType, vStreet, vId1, v1stFlrSF, v2ndFlrSF, v3SsnPorch, vBedroomAbvGr, vBsmtFinSF1, vBsmtFinSF2, vBsmtFullBath, vBsmtHalfBath, vBsmtUnfSF, vEnclosedPorch, vFireplaces, vFullBath, vGarageArea, vGarageCars, vGarageYrBlt, vGrLivArea, vHalfBath, vKitchenAbvGr, vLotArea, vLotFrontage, vLowQualFinSF, vMasVnrArea, vMiscVal, vMoSold, vOpenPorchSF, vOverallCond, vOverallQual, vPoolArea, vScreenPorch, vTotalBsmtSF, vTotRmsAbvGrd, vWoodDeckSF, vYearBuilt, vYearRemodAdd, vYrSold, 3, 5, 5, 5, 7, 7, 5, 2, 7, 2, 4, 4, 11, 11, 4, 5, 6, 5, 6, 4, 4, 5, 6, 3, 5, 8, 4, 4, 3, 5, 4, 5, 3, 14, 5, 24, 3, 2, 3, 5, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, FALSE, 12.24769, 12.10901, 12.31717, 11.8494, 12.42922, 11.8706, 12.6346, 12.20607, 11.77452, 11.67844, 11.77144, 12.7513, 11.87757, 12.54076, 11.964, 11.79056, 11.9117, 11.40756, 11.97666, 11.84223, 12.6925, 11.8451, 12.34583, 11.77452, 11.94471, 12.4541, 11.81155, 12.63134, 12.24289, 11.13459, 10.59663, 11.91405, 12.10016, 12.01673, 12.53358, 12.6411, 11.88449, 11.93819, 11.5991, 11.31447, 11.98293, 12.04355, 11.87757, 11.77721, 11.85652, 12.67576, 12.38709, 12.42802, 11.63514, 11.75194, 12.08391, 11.64833, 11.60824, 12.861, 11.77529, 12.10349, 12.05815, 12.18842, 12.99175, 11.73527, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
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Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 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0, 2, 2, 0, 5, 6, 6, 4, 2, 5, 6, 1, 1, 2, 2, 6, 2, 3, 6, 3, 0, 2, 0, 1, 2, 2, 5, 4, 0, 2, 5, 1, 2, 3, 0, 6, 4, 0, 1, 6, 1, 2, 6, 2, 6, 3, 6, 6, 6, 2, 2, 6, 0, 6, 2, 5, 0, 4, 5, 6, 1, 5, 0, 6, 2, 2, 2, 6, 6, 6, 1, 6, 6, 6, 2, 6, 5, 2, 6, 1, 2, 0, 1, 0, 1, 2, 0, 6, 2, 3, 6, 2, 5, 2, 2, 0, 6, 0, 6, 0, 2, 6, 6, 3, 6, 2, 0, 6, 6, 2, 6, 0, 6, 6, 0, 6, 0, 0, 6, 0, 0, 6, 1, 6, 3, 2, 0, 5, 3, 5, 6, 2, 3, 6, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 5, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 6, 1, 6, 1, 6, 5, 2, 5, 0, 1, 1, 2, 0, 0, 0, 6, 2, 2, 5, 0, 1, 6, 1, 0, 6, 2, 6, 6, 2, 6, 4, 5, 0, 2, 2, 6, 5, 2, 0, 5, 2, 6, 4, 4, 6, 2, 6, 1, 1, 2, 2, 6, 3, 2, 2, 2, 5, 0, 3, 6, 0, 5, 6, 4, 2, 6, 5, 5, 2, 6, 0, 0, 1, 6, 2, 6, 6, 2, 2, 2, 3, 1, 6, 6, 0, 5, 6, 3, 6, 6, 1, 6, 2, 6, 6, 2, 5, 0, 2, 6, 2, 2, 2, 2, 6, 2, 6, 6, 0, 3, 2, 6, 2, 6, 2, 1, 2, 2, 1, 5, 2, 0, 2, 0, 3, 2, 2, 6, 2, 2, 1, 0, 1, 2, 5, 6, 6, 1, 5, 2, 6, 2, 0, 1, 2, 3, 6, 6, 6, 2, 2, 2, 2, 5, 2, 0, 4, 5, 6, 1, 6, 6, 6, 6, 2, 6, 0, 6, 6, 1, 6, 2, 6, 1, 2, 6, 3, 2, 5, 6, 2, 1, 0, 2, 5, 0, 6, 6, 6, 5, 1, 5, 2, 2, 6, 2, 6, 2, 2, 0, 2, 2, 2, 6, 6, 2, 3, 3, 2, 2, 2, 6, 6, 6, 2, 4, 2, 2, 6, 6, 6, 6, 2, 0, 2, 6, 6, 1, 2, 0, 2, 2, 0, 6, 2, 0, 2, 2, 6, 1, 2, 2, 0, 1, 6, 5, 4, 6, 2, 6, 6, 2, 6, 0, 2, 2, 2, 6, 2, 4, 6, 6, 2, 6, 2, 2, 2, 5, 0, 3, 5, 3, 2, 2, 3, 6, 2, 0, 2, 0, 2, 3, 0, 5, 6, 2, 2, 0, 4, 2, 6, 0, 6, 2, 6, 5, 3, 2, 6, 3, 2, 0, 2, 6, 6, 6, 6, 1, 6, 0, 2, 3, 2, 6, 3, 6, 0, 2, 0, 6, 0, 2, 6, 5, 6, 6, 1, 2, 2, 2, 6, 6, 6, 6, 6, 2, 0, 2, 3, 6, 5, 6, 2, 5, 5, 1, 5, 1, 6, 1, 1, 6, 5, 6, 6, 0, 0, 1, 6, 6, 2, 6, 5, 5, 0, 0, 2, 6, 6, 1, 6, 1, 2, 1, 6, 1, 6, 0, 4, 2, 6, 2, 6, 5, 6, 2, 0, 2, 0, 0, 0, 3, 6, 6, 1, 2, 3, 6, 0, 1, 6, 3, 2, 1, 4, 1, 0, 4, 2, 1, 0, 1, 6, 6, 2, 5, 2, 5, 1, 6, 5, 0, 5, 1, 2, 6, 1, 0, 1, 0, 2, 0, 2, 3, 1, 0, 6, 1, 6, 6, 2, 1, 6, 2, 2, 6, 2, 2, 2, 6, 5, 0, 2, 6, 2, 3, 0, 2, 6, 0, 0, 1, 2, 0, 2, 5, 0, 5, 2, 0, 1, 0, 0, 6, 2, 6, 5, 0, 6, 0, 6, 2, 6, 6, 6, 2, 6, 2, 3, 5, 0, 2, 6, 6, 4, 0, 6, 2, 3, 6, 2, 1, 1, 6, 2, 0, 5, 6, 6, 2, 4, 6, 2, 6, 2, 2, 3, 1, 6, 6, 6, 4, 6, 0, 1, 2, 2, 2, 6, 2, 2, 2, 3, 2, 0, 3, 5, 2, 5, 1, 6, 2, 2, 2, 6, 4, 2, 6, 6, 2, 5, 2, 0, 2, 0, 4, 2, 2, 4, 4, 6, 6, 5, 5, 2, 0, 2, 2, 2, 5, 2, 6, 6, 1, 1, 2, 6, 2, 0, 0, 1, 5, 6, 1, 6, 1, 0, 1, 2, 2, 0, 0, 6, 1, 0, 2, 1, 6, 6, 2, 4, 1, 5, 2, 1, 2, 6, 6, 1, 0, 5, 1, 5, 0, 6, 2, 2, 6, 6, 2, 2, 0, 2, 1, 5, 2, 2, 1, 6, 3, 6, 2, 6, 6, 6, 6, 6, 2, 6, 2, 1, 1, 6, 2, 6, 6, 1, 6, 0, 1, 0, 0, 2, 2, 1, 6, 2, 5, 6, 0, 6, 1, 0, 0, 0, 0, 0, 2, 6, 0, 0, 1, 1, 2, 0, 6, 6, 2, 5, 2, 0, 0, 6, 5, 5, 2, 0, 5, 6, 4, 3, 2, 2, 5, 5, 1, 1, 2, 6, 6, 1, 6, 6, 2, 0, 6, 6, 6, 6, 5, 6, 6, 6, 6, 0, 0, 5, 2, 5, 2, 6, 2, 5, 2, 1, 5, 4, 2, 4, 6, 5, 1, 5, 3, 2, 2, 6, 0, 2, 0, 2, 0, 4, 5, 6, 6, 6, 6, 6, 2, 2, 6, 2, 2, 6, 6, 6, 2, 5, 1, 0, 6, 1, 3, 6, 3, 2, 6, 2, 0, 6, 5, 6, 6, 2, 2, 6, 6, 5, 1, 2, 6, 1, 0, 6, 5, 1, 0, 2, 6, 2, 0, 3, 6, 6, 6, 0, 5, 2, 6, 2, 0, 6, 2, 5, 1, 0, 2, 2, 3, 2, 1, 2, 6, 6, 2, 6, 0, 2, 2, 2, 2, 2, 6, 5, 0, 6, 6, 6, 0, 0, 4, 2, 3, 6, 6, 5, 0, 3, 6, 6, 0, 0, 6, 3, 0, 6, 6, 2, 5, 6, 2, 6, 6, 6, 0, 1, 2, 2, 3, 3, 5, 6, 2, 2, 6, 5, 2, 2, 2, 6, 0, 6, 6, 6, 2, 2, 0, 2, 1, 0, 1, 2, 2, 6, 6, 5, 3, 1, 6, 5, 1, 6, 6, 5, 1, 1, 5, 2, 0, 2, 6, 0, 6, 2, 6, 1, 6, 5, 1, 6, 2, 6, 2, 6, 2, 2, 0, 6, 6, 2, 1, 4, 2, 6, 0, 6, 2, 1, 5, 0, 0, 2, 6, 0, 6, 2, 1, 1, 1, 6, 3, 6, 6, 0, 6, 0, 2, 2, 2, 6, 2, 2, 6, 6, 3, 5, 2, 6, 2, 6, 6, 2, 6, 2, 6, 0, 2, 2, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 0, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 3, 1, 1, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 5, 3, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 1, 6, 6, 6, 6, 6, 5, 5, 3, 6, 6, 1, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 4, 0, 6, 6, 0, 6, 3, 6, 6, 5, 6, 6, 2, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 1, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 1, 6, 6, 5, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 5, 6, 4, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 5, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 3, 6, 3, 6, 6, 5, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 5, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 3, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 4, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 1, 6, 6, 6, 2, 3, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6, 1, 6, 6, 6, 1, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 5, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 5, 6, 6, 6, 4, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 5, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 3, 4, 6, 4, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 0, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 2, 5, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 3, 2, 2, 2, 4, 2, 2, 0, 2, 4, 4, 4, 0, 4, 2, 4, 4, 4, 3, 4, 4, 0, 4, 2, 2, 4, 2, 4, 0, 4, 4, 4, 4, 0, 4, 0, 0, 2, 4, 4, 3, 4, 4, 2, 2, 4, 0, 0, 2, 4, 4, 2, 4, 2, 0, 4, 4, 2, 2, 0, 4, 2, 4, 2, 4, 2, 0, 2, 2, 4, 4, 2, 4, 2, 4, 1, 2, 4, 4, 4, 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325, 326, 327, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 382, 383, 384, 385, 386, 387, 388, 389, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 457, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 498, 499, 500, 501, 502, 503, 504, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 521, 522, 523, 524, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 597, 598, 599, 600, 601, 602, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 621, 622, 623, 624, 625, 626, 627, 628, 629, 631, 632, 633, 634, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 677, 678, 679, 680, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 712, 713, 714, 715, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 741, 742, 743, 744, 745, 746, 748, 749, 751, 752, 753, 754, 756, 757, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 815, 816, 817, 818, 819, 820, 822, 823, 824, 825, 826, 827, 828, 830, 832, 833, 834, 835, 837, 838, 839, 840, 842, 843, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 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46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 79, 80, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 124, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 181, 182, 183, 184, 185, 186, 187, 190, 191, 192, 194, 196, 197, 198, 199, 200, 201, 202, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 228, 230, 231, 233, 234, 236, 237, 238, 239, 240, 241, 242, 244, 245, 247, 248, 249, 250, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 283, 286, 287, 288, 289, 290, 292, 293, 294, 295, 296, 297, 298, 299, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 327, 328, 329, 331, 332, 334, 336, 337, 338, 339, 340, 341, 345, 346, 347, 349, 351, 352, 353, 354, 355, 356, 358, 359, 360, 361, 362, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 412, 413, 414, 415, 416, 417, 418, 419, 421, 422, 423, 424, 425, 426, 427, 428, 429, 431, 433, 435, 436, 437, 438, 439, 440, 442, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 466, 467, 468, 469, 471, 473, 475, 476, 477, 478, 479, 480, 481, 482, 484, 485, 486, 487, 491, 492, 493, 494, 495, 496, 497, 498, 499, 501, 502, 503, 506, 507, 508, 509, 510, 512, 513, 514, 515, 516, 517, 518, 519, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 536, 537, 538, 539, 540, 541, 542, 544, 545, 546, 547, 548, 549, 551, 552, 553, 554, 555, 556, 557, 558, 560, 561, 562, 563, 564, 565, 566, 567, 568, 571, 572, 573, 574, 575, 576, 577, 579, 580, 581, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 594, 595, 596, 598, 600, 601, 602, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 615, 616, 617, 618, 619, 620, 621, 622, 624, 625, 626, 627, 628, 629, 630, 632, 633, 636, 638, 641, 642, 643, 644, 645, 646, 647, 648, 650, 651, 652, 653, 654, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 676, 677, 678, 679, 681, 682, 683, 684, 686, 688, 691, 692, 693, 694, 695, 696, 697, 698, 700, 701, 702, 704, 706, 708, 709, 710, 711, 714, 715, 716, 717, 718, 719, 720, 722, 723, 724, 725, 726, 727, 729, 731, 732, 733, 734, 735, 737, 739, 740, 741, 742, 743, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 756, 757, 759, 760, 761, 762, 763, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 776, 777, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 812, 813, 814, 815, 816, 817, 818, 820, 822, 823, 824, 825, 826, 827, 828, 830, 832, 833, 834, 835, 836, 838, 839, 840, 841, 842, 844, 845, 846, 847, 848, 849, 852, 853, 854, 855, 856, 857, 858, 859, 860, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 887, 888, 889, 890, 891, 892, 893, 895, 896, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 911, 912, 916, 917, 918, 919, 920, 922, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 941, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 957, 958, 960, 961, 963, 964, 965, 966, 967, 968, 970, 973, 974, 976, 978, 979, 980, 981, 982, 983, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1005, 1006, 1008, 1009, 1010, 1012, 1013, 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400, 432, 443, 465, 470, 472, 474, 490, 504, 511, 543, 550, 559, 578, 593, 597, 603, 614, 623, 639, 640, 680, 685, 687, 689, 690, 699, 707, 712, 721, 730, 744, 755, 764, 775, 790, 811, 819, 831, 850, 851, 885, 914, 923, 956, 962, 972, 977, 1004, 1007, 1017, 1019, 1023, 1039, 1056, 1060, 1068, 1078, 1086, 1089, 61, 88, 93, 110, 124, 174, 239, 291, 339, 341, 352, 365, 383, 410, 439, 488, 531, 555, 630, 635, 636, 662, 676, 740, 747, 750, 771, 789, 883, 966, 986, 998, 1012, 1014, 1034, 1072, 3, 62, 81, 95, 171, 172, 175, 190, 233, 262, 269, 314, 320, 355, 381, 390, 408, 420, 461, 466, 534, 544, 545, 566, 586, 592, 607, 631, 639, 661, 695, 697, 702, 738, 745, 764, 780, 824, 828, 856, 880, 888, 911, 920, 932, 938, 954, 961, 989, 1005, 1023, 1032, 17, 39, 90, 102, 156, 182, 259, 342, 362, 371, 392, 520, 532, 533, 553, 646, 705, 736, 749, 778, 868, 894, 897, 984, 1000, 1011, 1035, 1045, 1048, 1049, 1090, 375, 398, 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 89, 91, 92, 94, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 173, 176, 177, 178, 179, 180, 181, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 234, 235, 236, 237, 238, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 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289, 337, 353, 362, 553, 588, 592, 593, 616, 619, 710, 731, 747, 751, 769, 820, 822, 832, 850, 851, 892, 902, 921, 936, 947, 952, 958, 964, 986, 1069, 18, 57, 60, 105, 161, 164, 168, 191, 193, 200, 203, 216, 236, 252, 264, 299, 309, 321, 332, 333, 348, 374, 437, 465, 481, 498, 519, 534, 549, 554, 559, 567, 590, 640, 673, 687, 690, 699, 721, 739, 750, 787, 807, 811, 926, 933, 971, 1078, 1080, 1088, 6, 34, 35, 45, 65, 86, 108, 141, 148, 158, 162, 199, 271, 305, 315, 323, 343, 377, 385, 401, 450, 472, 480, 482, 501, 508, 525, 574, 600, 603, 633, 661, 670, 704, 714, 737, 753, 754, 768, 802, 829, 831, 877, 879, 886, 909, 937, 1008, 1019, 1020, 1042, 1056, 1089, 11, 20, 31, 47, 58, 62, 71, 92, 119, 145, 159, 179, 182, 218, 219, 220, 229, 249, 257, 270, 281, 290, 317, 320, 336, 349, 369, 381, 382, 408, 468, 477, 492, 511, 540, 544, 552, 585, 595, 631, 639, 656, 664, 677, 689, 702, 707, 774, 776, 790, 824, 838, 880, 890, 903, 906, 922, 932, 938, 949, 989, 993, 999, 1002, 1004, 1013, 1021, 1023, 1046, 1048, 1049, 1074, 1087, 13, 25, 32, 38, 82, 112, 117, 167, 196, 238, 251, 261, 272, 275, 278, 285, 324, 350, 363, 399, 415, 428, 443, 461, 473, 485, 532, 566, 578, 597, 613, 618, 650, 686, 688, 708, 726, 727, 756, 789, 793, 866, 875, 930, 934, 963, 965, 977, 980, 982, 994, 1050, 1051, 27, 48, 151, 240, 282, 292, 389, 409, 440, 453, 478, 523, 527, 591, 678, 724, 765, 805, 825, 864, 960, 973, 1027, 1036, 1038, 1058, 87, 103, 178, 211, 212, 283, 412, 460, 507, 515, 568, 572, 581, 644, 698, 762, 798, 803, 914, 157, 378, 819, 855, 898, 987, 3, 11, 17, 20, 28, 35, 40, 44, 51, 53, 57, 58, 60, 69, 81, 85, 90, 91, 96, 110, 119, 120, 125, 128, 129, 130, 134, 137, 141, 144, 145, 149, 152, 154, 156, 159, 169, 172, 177, 181, 184, 185, 193, 197, 202, 213, 215, 217, 219, 220, 222, 232, 242, 245, 246, 247, 255, 262, 266, 270, 281, 286, 287, 290, 293, 295, 300, 302, 303, 309, 310, 312, 314, 320, 323, 327, 338, 342, 345, 349, 351, 354, 358, 359, 364, 370, 376, 381, 386, 393, 401, 403, 411, 416, 436, 447, 448, 450, 451, 454, 465, 480, 481, 483, 488, 491, 492, 506, 511, 512, 522, 525, 534, 538, 544, 545, 555, 556, 557, 559, 561, 564, 569, 571, 577, 585, 595, 596, 598, 600, 602, 607, 616, 624, 630, 639, 664, 665, 668, 669, 672, 676, 692, 693, 695, 696, 697, 700, 701, 702, 713, 719, 720, 735, 736, 737, 752, 753, 764, 768, 771, 776, 777, 779, 781, 804, 806, 808, 810, 814, 816, 824, 829, 831, 851, 854, 859, 868, 883, 886, 892, 896, 899, 902, 903, 907, 908, 912, 916, 922, 924, 929, 935, 938, 940, 946, 948, 951, 954, 969, 970, 975, 976, 986, 989, 990, 993, 995, 996, 998, 1009, 1019, 1021, 1029, 1030, 1032, 1033, 1040, 1046, 1054, 1056, 1063, 1068, 1072, 1076, 1077, 1078, 1083, 1084, 1088, 1089, 1093, 1, 6, 13, 15, 21, 23, 34, 41, 42, 47, 49, 50, 54, 61, 62, 65, 67, 70, 71, 83, 89, 93, 94, 97, 104, 106, 108, 112, 113, 114, 115, 117, 121, 126, 127, 132, 136, 150, 163, 164, 167, 168, 170, 175, 176, 179, 180, 182, 190, 191, 196, 206, 208, 226, 238, 241, 248, 249, 251, 253, 261, 269, 274, 278, 280, 284, 285, 289, 296, 297, 298, 301, 305, 306, 317, 321, 322, 325, 330, 331, 336, 346, 350, 355, 357, 360, 374, 377, 382, 384, 392, 394, 397, 398, 404, 408, 415, 417, 418, 428, 432, 438, 443, 449, 452, 455, 466, 467, 468, 471, 473, 474, 475, 477, 479, 484, 486, 487, 496, 499, 500, 502, 513, 514, 518, 521, 523, 524, 526, 528, 529, 533, 541, 543, 546, 547, 573, 574, 580, 582, 597, 601, 608, 609, 611, 613, 618, 623, 626, 628, 631, 633, 635, 641, 643, 645, 649, 660, 666, 673, 679, 683, 685, 686, 687, 688, 689, 691, 706, 708, 716, 731, 734, 740, 742, 751, 759, 773, 774, 778, 780, 789, 791, 792, 793, 796, 799, 801, 813, 822, 836, 843, 845, 849, 850, 852, 860, 866, 867, 875, 876, 880, 881, 888, 890, 900, 904, 906, 913, 915, 918, 920, 926, 932, 942, 943, 947, 950, 955, 957, 958, 962, 965, 977, 978, 988, 992, 1001, 1003, 1006, 1012, 1014, 1018, 1022, 1025, 1028, 1034, 1050, 1051, 1052, 1059, 1062, 1069, 1070, 1074, 1075, 1079, 1082, 0, 2, 4, 8, 9, 10, 12, 14, 18, 22, 29, 30, 31, 32, 39, 43, 55, 59, 76, 77, 82, 105, 107, 122, 123, 135, 138, 148, 151, 153, 155, 160, 161, 165, 173, 174, 183, 189, 194, 201, 203, 207, 209, 210, 216, 218, 227, 235, 252, 256, 258, 259, 264, 265, 267, 268, 271, 279, 291, 304, 307, 326, 333, 334, 335, 337, 343, 348, 352, 361, 367, 371, 388, 389, 390, 400, 402, 406, 407, 409, 414, 420, 422, 423, 424, 427, 430, 431, 433, 434, 441, 442, 444, 456, 457, 458, 463, 469, 472, 476, 490, 493, 497, 501, 508, 520, 527, 530, 531, 535, 536, 537, 548, 550, 551, 554, 558, 562, 563, 566, 570, 575, 578, 579, 583, 586, 589, 590, 592, 594, 599, 604, 617, 619, 620, 621, 629, 638, 640, 646, 647, 650, 653, 654, 656, 657, 663, 667, 674, 682, 690, 699, 709, 710, 712, 717, 718, 723, 732, 741, 744, 745, 758, 765, 767, 784, 788, 794, 797, 800, 802, 805, 811, 817, 820, 825, 826, 830, 834, 837, 838, 839, 840, 841, 842, 844, 848, 856, 864, 872, 885, 887, 893, 895, 919, 921, 923, 925, 927, 934, 953, 961, 967, 973, 980, 982, 983, 985, 1002, 1005, 1010, 1020, 1023, 1024, 1027, 1037, 1041, 1043, 1047, 1055, 1061, 1067, 1080, 1091, 1092, 5, 7, 19, 25, 36, 37, 46, 48, 56, 64, 72, 75, 79, 80, 84, 86, 87, 88, 92, 95, 102, 116, 124, 131, 133, 139, 143, 146, 166, 178, 186, 187, 188, 192, 195, 198, 199, 204, 205, 212, 221, 223, 224, 225, 229, 231, 243, 257, 260, 273, 275, 282, 283, 292, 294, 299, 308, 311, 313, 315, 316, 318, 319, 328, 329, 332, 339, 341, 347, 356, 362, 363, 365, 366, 373, 375, 379, 383, 387, 391, 396, 399, 405, 410, 421, 425, 426, 429, 435, 437, 439, 440, 445, 453, 459, 460, 461, 462, 464, 478, 482, 485, 489, 494, 495, 498, 504, 505, 507, 509, 510, 515, 516, 517, 519, 540, 542, 549, 552, 553, 568, 572, 576, 581, 584, 587, 588, 591, 593, 605, 606, 610, 612, 622, 632, 636, 637, 642, 644, 651, 652, 659, 661, 662, 670, 671, 675, 677, 678, 681, 694, 707, 715, 722, 724, 725, 726, 727, 728, 729, 733, 738, 739, 743, 746, 747, 749, 754, 755, 756, 760, 761, 763, 770, 775, 782, 783, 785, 790, 798, 803, 807, 809, 821, 823, 827, 828, 833, 846, 847, 853, 857, 858, 863, 865, 870, 873, 874, 877, 879, 882, 884, 889, 891, 894, 897, 901, 909, 911, 914, 917, 928, 930, 931, 933, 936, 937, 941, 944, 945, 952, 956, 963, 966, 968, 971, 974, 979, 981, 984, 991, 994, 997, 1000, 1004, 1007, 1008, 1013, 1015, 1016, 1017, 1031, 1035, 1036, 1038, 1039, 1042, 1044, 1045, 1048, 1057, 1058, 1064, 1066, 1071, 1073, 1087, 1090, 16, 24, 26, 27, 33, 38, 45, 52, 63, 66, 68, 73, 74, 78, 98, 99, 100, 101, 103, 109, 111, 118, 140, 142, 147, 157, 158, 162, 171, 200, 211, 214, 228, 230, 233, 234, 236, 237, 239, 240, 244, 250, 254, 263, 272, 276, 277, 288, 324, 340, 344, 353, 368, 369, 372, 378, 380, 385, 395, 412, 413, 419, 446, 470, 503, 532, 539, 560, 565, 567, 603, 614, 615, 625, 627, 634, 648, 655, 658, 680, 684, 698, 703, 704, 705, 711, 714, 721, 730, 748, 750, 757, 762, 766, 769, 772, 786, 787, 795, 812, 815, 818, 819, 832, 835, 855, 861, 862, 869, 871, 878, 898, 905, 910, 939, 949, 959, 960, 964, 972, 987, 999, 1011, 1026, 1049, 1053, 1060, 1065, 1081, 1085, 1086, 1094, NA, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
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1, 1, 1, 0.1, gaussian, 3, 10, 1, 500, 1095, 0.75, log, vSalePrice, 0.1, Grvl, no-disponible, Pave, 1Fam, 2fmCon, Duplex, Twnhs, TwnhsE, Fa, Gd, no-disponible, Otros, TA, Av, Gd, Mn, No, no-disponible, ALQ, BLQ, GLQ, LwQ, no-disponible, Rec, Unf, ALQ, BLQ, GLQ, LwQ, no-disponible, Rec, Unf, Ex, Fa, Gd, no-disponible, TA, N, Y, Artery, Feedr, Norm, Otros, PosN, RRAe, RRAn, Norm, Otros, FuseA, FuseF, Otros, SBrkr, Fa, Gd, Otros, TA, AsbShng, BrkFace, CemntBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, WdShing, AsbShng, BrkFace, CmentBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, Wd Shng, Ex, Fa, Gd, TA, GdPrv, GdWo, MnPrv, MnWw, no-disponible, Ex, Fa, Gd, no-disponible, Po, TA, BrkTil, CBlock, Otros, PConc, Slab, Maj1, Min1, Min2, Mod, Otros, Typ, Fa, no-disponible, Otros, TA, Fin, no-disponible, RFn, Unf, Fa, Gd, no-disponible, Otros, TA, Attchd, Basment, BuiltIn, Detchd, no-disponible, Otros, GasA, GasW, Otros, Ex, Fa, Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 8, 0, 0, 0, 0, 218.6, 383.5, 525.6, 655, 806.4, 1065.5, 5644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117.2, 1474, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 74.9, 172, 280, 374.6, 477.5, 604.4, 736, 896, 1232, 2336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 552, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 0, 240, 295.6, 384, 440, 480, 516, 560, 620.2, 757.1, 1418, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 0, 1928, 1954, 1962, 1970, 1977, 1990, 1998, 2003, 2006, 2010, 334, 912, 1066.6, 1208, 1339, 1464, 1578, 1709.3, 1869, 2158.3, 5642, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1300, 5000, 7078.4, 8063.7, 8793.4, 9478.5, 10198.2, 11066.5, 12205.8, 14381.7, 215245, 0, 0, 24, 50, 60, 63, 70, 75, 80, 92, 313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 16, 116, 205.2, 335, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15500, 1, 3, 4, 5, 6, 6, 7, 7, 8, 10, 12, 0, 0, 0, 0, 0, 25, 40, 57, 83.2, 130, 547, 1, 5, 5, 5, 5, 5, 5, 6, 7, 7, 9, 1, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 738, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 636.9, 755.8, 840, 910, 991.5, 1088, 1216, 1391.2, 1602.2, 6110, 2, 5, 5, 6, 6, 6, 7, 7, 8, 9, 14, 0, 0, 0, 0, 0, 0, 100, 144, 192, 262, 857, 1872, 1924.9, 1947.8, 1958, 1965, 1973, 1984, 1997.3, 2003, 2006, 2010, 1950, 1950, 1961.8, 1971, 1980, 1994, 1998, 2002, 2005, 2006, 2010, 2006, 2006, 2006, 2007, 2007, 2008, 2008, 2009, 2009, 2010, 2010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, vAlley, vBldgType, vBsmtCond, vBsmtExposure, vBsmtFinType1, vBsmtFinType2, vBsmtQual, vCentralAir, vCondition1, vCondition2, vElectrical, vExterCond, vExterior1st, vExterior2nd, vExterQual, vFence, vFireplaceQu, vFoundation, vFunctional, vGarageCond, vGarageFinish, vGarageQual, vGarageType, vHeating, vHeatingQC, vHouseStyle, vKitchenQual, vLandContour, vLandSlope, vLotConfig, vLotShape, vMasVnrType, vMiscFeature, vMSSubClass, vMSZoning, vNeighborhood, vPavedDrive, vPoolQC, vRoofMatl, vRoofStyle, vSaleCondition, vSaleType, vStreet, vId1, v1stFlrSF, v2ndFlrSF, v3SsnPorch, vBedroomAbvGr, vBsmtFinSF1, vBsmtFinSF2, vBsmtFullBath, vBsmtHalfBath, vBsmtUnfSF, vEnclosedPorch, vFireplaces, vFullBath, vGarageArea, vGarageCars, vGarageYrBlt, vGrLivArea, vHalfBath, vKitchenAbvGr, vLotArea, vLotFrontage, vLowQualFinSF, vMasVnrArea, vMiscVal, vMoSold, vOpenPorchSF, vOverallCond, vOverallQual, vPoolArea, vScreenPorch, vTotalBsmtSF, vTotRmsAbvGrd, vWoodDeckSF, vYearBuilt, vYearRemodAdd, vYrSold, 3, 5, 5, 5, 7, 7, 5, 2, 7, 2, 4, 4, 11, 11, 4, 5, 6, 5, 6, 4, 4, 5, 6, 3, 5, 8, 4, 4, 3, 5, 4, 5, 3, 14, 5, 24, 3, 2, 3, 5, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, FALSE, 12.24769, 12.10901, 12.31717, 11.8494, 12.42922, 11.8706, 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6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 4, 0, 6, 6, 0, 6, 3, 6, 6, 5, 6, 6, 2, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 1, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 1, 6, 6, 5, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 5, 6, 4, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 5, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 3, 6, 3, 6, 6, 5, 6, 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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
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FuseA, FuseF, Otros, SBrkr, Fa, Gd, Otros, TA, AsbShng, BrkFace, CemntBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, WdShing, AsbShng, BrkFace, CmentBd, HdBoard, MetalSd, Otros, Plywood, Stucco, VinylSd, Wd Sdng, Wd Shng, Ex, Fa, Gd, TA, GdPrv, GdWo, MnPrv, MnWw, no-disponible, Ex, Fa, Gd, no-disponible, Po, TA, BrkTil, CBlock, Otros, PConc, Slab, Maj1, Min1, Min2, Mod, Otros, Typ, Fa, no-disponible, Otros, TA, Fin, no-disponible, RFn, Unf, Fa, Gd, no-disponible, Otros, TA, Attchd, Basment, BuiltIn, Detchd, no-disponible, Otros, GasA, GasW, Otros, Ex, Fa, Gd, Otros, TA, 1.5Fin, 1.5Unf, 1Story, 2.5Unf, 2Story, Otros, SFoyer, SLvl, Ex, Fa, Gd, TA, Bnk, HLS, Low, Lvl, Gtl, Mod, Sev, Corner, CulDSac, FR2, Inside, Otros, IR1, IR2, Otros, Reg, BrkCmn, BrkFace, None, Otros, Stone, no-disponible, Otros, Shed, nivel_120, nivel_160, nivel_190, nivel_20, nivel_30, nivel_45, nivel_50, nivel_60, nivel_70, nivel_75, nivel_80, nivel_85, nivel_90, Otros, FV, Otros, RH, RL, RM, Blmngtn, BrDale, BrkSide, ClearCr, CollgCr, Crawfor, Edwards, Gilbert, IDOTRR, MeadowV, Mitchel, NAmes, NoRidge, NridgHt, NWAmes, OldTown, Otros, Sawyer, SawyerW, Somerst, StoneBr, SWISU, Timber, Veenker, N, P, Y, no-disponible, Otros, CompShg, Otros, Tar&Grv, Flat, Gable, Gambrel, Hip, Otros, Abnorml, Alloca, Family, Normal, Otros, Partial, COD, New, Otros, WD, Otros, Pave, 1, 146.9, 292.8, 438.7, 584.6, 730.5, 876.4, 1022.3, 1168.2, 1314.1, 1460, 334, 756.9, 848, 915.7, 1000.2, 1087, 1182, 1314, 1482.4, 1680, 4692, 0, 0, 0, 0, 0, 0, 455.4, 672, 796.2, 954.2, 2065, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 508, 0, 2, 2, 3, 3, 3, 3, 3, 3, 4, 8, 0, 0, 0, 0, 218.6, 383.5, 525.6, 655, 806.4, 1065.5, 5644, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117.2, 1474, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 74.9, 172, 280, 374.6, 477.5, 604.4, 736, 896, 1232, 2336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 552, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 0, 240, 295.6, 384, 440, 480, 516, 560, 620.2, 757.1, 1418, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 0, 1928, 1954, 1962, 1970, 1977, 1990, 1998, 2003, 2006, 2010, 334, 912, 1066.6, 1208, 1339, 1464, 1578, 1709.3, 1869, 2158.3, 5642, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1300, 5000, 7078.4, 8063.7, 8793.4, 9478.5, 10198.2, 11066.5, 12205.8, 14381.7, 215245, 0, 0, 24, 50, 60, 63, 70, 75, 80, 92, 313, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 572, 0, 0, 0, 0, 0, 0, 16, 116, 205.2, 335, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15500, 1, 3, 4, 5, 6, 6, 7, 7, 8, 10, 12, 0, 0, 0, 0, 0, 25, 40, 57, 83.2, 130, 547, 1, 5, 5, 5, 5, 5, 5, 6, 7, 7, 9, 1, 5, 5, 5, 6, 6, 6, 7, 7, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 738, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 636.9, 755.8, 840, 910, 991.5, 1088, 1216, 1391.2, 1602.2, 6110, 2, 5, 5, 6, 6, 6, 7, 7, 8, 9, 14, 0, 0, 0, 0, 0, 0, 100, 144, 192, 262, 857, 1872, 1924.9, 1947.8, 1958, 1965, 1973, 1984, 1997.3, 2003, 2006, 2010, 1950, 1950, 1961.8, 1971, 1980, 1994, 1998, 2002, 2005, 2006, 2010, 2006, 2006, 2006, 2007, 2007, 2008, 2008, 2009, 2009, 2010, 2010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, vAlley, vBldgType, vBsmtCond, vBsmtExposure, vBsmtFinType1, vBsmtFinType2, vBsmtQual, vCentralAir, vCondition1, vCondition2, vElectrical, vExterCond, vExterior1st, vExterior2nd, vExterQual, vFence, vFireplaceQu, vFoundation, vFunctional, vGarageCond, vGarageFinish, vGarageQual, vGarageType, vHeating, vHeatingQC, vHouseStyle, vKitchenQual, vLandContour, vLandSlope, vLotConfig, vLotShape, vMasVnrType, vMiscFeature, vMSSubClass, vMSZoning, vNeighborhood, vPavedDrive, vPoolQC, vRoofMatl, vRoofStyle, vSaleCondition, vSaleType, vStreet, vId1, v1stFlrSF, v2ndFlrSF, v3SsnPorch, vBedroomAbvGr, vBsmtFinSF1, vBsmtFinSF2, vBsmtFullBath, vBsmtHalfBath, vBsmtUnfSF, vEnclosedPorch, vFireplaces, vFullBath, vGarageArea, vGarageCars, vGarageYrBlt, vGrLivArea, vHalfBath, vKitchenAbvGr, vLotArea, vLotFrontage, vLowQualFinSF, vMasVnrArea, vMiscVal, vMoSold, vOpenPorchSF, vOverallCond, vOverallQual, vPoolArea, vScreenPorch, vTotalBsmtSF, vTotRmsAbvGrd, vWoodDeckSF, vYearBuilt, vYearRemodAdd, vYrSold, 3, 5, 5, 5, 7, 7, 5, 2, 7, 2, 4, 4, 11, 11, 4, 5, 6, 5, 6, 4, 4, 5, 6, 3, 5, 8, 4, 4, 3, 5, 4, 5, 3, 14, 5, 24, 3, 2, 3, 5, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, FALSE, 12.24769, 12.10901, 12.31717, 11.8494, 12.42922, 11.8706, 12.6346, 12.20607, 11.77452, 11.67844, 11.77144, 12.7513, 11.87757, 12.54076, 11.964, 11.79056, 11.9117, 11.40756, 11.97666, 11.84223, 12.6925, 11.8451, 12.34583, 11.77452, 11.94471, 12.4541, 11.81155, 12.63134, 12.24289, 11.13459, 10.59663, 11.91405, 12.10016, 12.01673, 12.53358, 12.6411, 11.88449, 11.93819, 11.5991, 11.31447, 11.98293, 12.04355, 11.87757, 11.77721, 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5, 6, 1, 6, 2, 2, 0, 2, 5, 2, 5, 6, 1, 6, 2, 6, 1, 2, 5, 1, 6, 6, 4, 6, 2, 2, 1, 2, 1, 6, 3, 0, 3, 2, 6, 6, 5, 1, 2, 0, 0, 0, 2, 0, 2, 6, 2, 3, 4, 6, 6, 6, 2, 6, 2, 2, 5, 0, 2, 6, 0, 0, 2, 2, 6, 2, 6, 0, 3, 2, 3, 6, 6, 0, 2, 5, 5, 2, 2, 0, 2, 1, 2, 6, 1, 2, 6, 6, 0, 0, 2, 6, 2, 5, 0, 2, 6, 2, 6, 3, 2, 0, 2, 1, 6, 3, 2, 0, 6, 6, 2, 2, 6, 6, 6, 5, 6, 2, 6, 3, 5, 6, 5, 2, 2, 4, 5, 6, 0, 3, 6, 2, 2, 3, 0, 1, 6, 3, 2, 5, 0, 6, 6, 3, 6, 1, 2, 2, 2, 6, 2, 6, 5, 1, 1, 6, 6, 5, 3, 0, 2, 2, 1, 1, 0, 6, 1, 2, 6, 0, 6, 2, 0, 6, 1, 2, 0, 0, 5, 0, 3, 2, 2, 6, 2, 2, 6, 2, 3, 0, 6, 1, 2, 5, 6, 6, 2, 5, 2, 2, 2, 0, 2, 2, 0, 5, 6, 6, 4, 2, 5, 6, 1, 1, 2, 2, 6, 2, 3, 6, 3, 0, 2, 0, 1, 2, 2, 5, 4, 0, 2, 5, 1, 2, 3, 0, 6, 4, 0, 1, 6, 1, 2, 6, 2, 6, 3, 6, 6, 6, 2, 2, 6, 0, 6, 2, 5, 0, 4, 5, 6, 1, 5, 0, 6, 2, 2, 2, 6, 6, 6, 1, 6, 6, 6, 2, 6, 5, 2, 6, 1, 2, 0, 1, 0, 1, 2, 0, 6, 2, 3, 6, 2, 5, 2, 2, 0, 6, 0, 6, 0, 2, 6, 6, 3, 6, 2, 0, 6, 6, 2, 6, 0, 6, 6, 0, 6, 0, 0, 6, 0, 0, 6, 1, 6, 3, 2, 0, 5, 3, 5, 6, 2, 3, 6, 2, 2, 6, 2, 2, 2, 2, 2, 6, 2, 5, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 6, 1, 6, 1, 6, 5, 2, 5, 0, 1, 1, 2, 0, 0, 0, 6, 2, 2, 5, 0, 1, 6, 1, 0, 6, 2, 6, 6, 2, 6, 4, 5, 0, 2, 2, 6, 5, 2, 0, 5, 2, 6, 4, 4, 6, 2, 6, 1, 1, 2, 2, 6, 3, 2, 2, 2, 5, 0, 3, 6, 0, 5, 6, 4, 2, 6, 5, 5, 2, 6, 0, 0, 1, 6, 2, 6, 6, 2, 2, 2, 3, 1, 6, 6, 0, 5, 6, 3, 6, 6, 1, 6, 2, 6, 6, 2, 5, 0, 2, 6, 2, 2, 2, 2, 6, 2, 6, 6, 0, 3, 2, 6, 2, 6, 2, 1, 2, 2, 1, 5, 2, 0, 2, 0, 3, 2, 2, 6, 2, 2, 1, 0, 1, 2, 5, 6, 6, 1, 5, 2, 6, 2, 0, 1, 2, 3, 6, 6, 6, 2, 2, 2, 2, 5, 2, 0, 4, 5, 6, 1, 6, 6, 6, 6, 2, 6, 0, 6, 6, 1, 6, 2, 6, 1, 2, 6, 3, 2, 5, 6, 2, 1, 0, 2, 5, 0, 6, 6, 6, 5, 1, 5, 2, 2, 6, 2, 6, 2, 2, 0, 2, 2, 2, 6, 6, 2, 3, 3, 2, 2, 2, 6, 6, 6, 2, 4, 2, 2, 6, 6, 6, 6, 2, 0, 2, 6, 6, 1, 2, 0, 2, 2, 0, 6, 2, 0, 2, 2, 6, 1, 2, 2, 0, 1, 6, 5, 4, 6, 2, 6, 6, 2, 6, 0, 2, 2, 2, 6, 2, 4, 6, 6, 2, 6, 2, 2, 2, 5, 0, 3, 5, 3, 2, 2, 3, 6, 2, 0, 2, 0, 2, 3, 0, 5, 6, 2, 2, 0, 4, 2, 6, 0, 6, 2, 6, 5, 3, 2, 6, 3, 2, 0, 2, 6, 6, 6, 6, 1, 6, 0, 2, 3, 2, 6, 3, 6, 0, 2, 0, 6, 0, 2, 6, 5, 6, 6, 1, 2, 2, 2, 6, 6, 6, 6, 6, 2, 0, 2, 3, 6, 5, 6, 2, 5, 5, 1, 5, 1, 6, 1, 1, 6, 5, 6, 6, 0, 0, 1, 6, 6, 2, 6, 5, 5, 0, 0, 2, 6, 6, 1, 6, 1, 2, 1, 6, 1, 6, 0, 4, 2, 6, 2, 6, 5, 6, 2, 0, 2, 0, 0, 0, 3, 6, 6, 1, 2, 3, 6, 0, 1, 6, 3, 2, 1, 4, 1, 0, 4, 2, 1, 0, 1, 6, 6, 2, 5, 2, 5, 1, 6, 5, 0, 5, 1, 2, 6, 1, 0, 1, 0, 2, 0, 2, 3, 1, 0, 6, 1, 6, 6, 2, 1, 6, 2, 2, 6, 2, 2, 2, 6, 5, 0, 2, 6, 2, 3, 0, 2, 6, 0, 0, 1, 2, 0, 2, 5, 0, 5, 2, 0, 1, 0, 0, 6, 2, 6, 5, 0, 6, 0, 6, 2, 6, 6, 6, 2, 6, 2, 3, 5, 0, 2, 6, 6, 4, 0, 6, 2, 3, 6, 2, 1, 1, 6, 2, 0, 5, 6, 6, 2, 4, 6, 2, 6, 2, 2, 3, 1, 6, 6, 6, 4, 6, 0, 1, 2, 2, 2, 6, 2, 2, 2, 3, 2, 0, 3, 5, 2, 5, 1, 6, 2, 2, 2, 6, 4, 2, 6, 6, 2, 5, 2, 0, 2, 0, 4, 2, 2, 4, 4, 6, 6, 5, 5, 2, 0, 2, 2, 2, 5, 2, 6, 6, 1, 1, 2, 6, 2, 0, 0, 1, 5, 6, 1, 6, 1, 0, 1, 2, 2, 0, 0, 6, 1, 0, 2, 1, 6, 6, 2, 4, 1, 5, 2, 1, 2, 6, 6, 1, 0, 5, 1, 5, 0, 6, 2, 2, 6, 6, 2, 2, 0, 2, 1, 5, 2, 2, 1, 6, 3, 6, 2, 6, 6, 6, 6, 6, 2, 6, 2, 1, 1, 6, 2, 6, 6, 1, 6, 0, 1, 0, 0, 2, 2, 1, 6, 2, 5, 6, 0, 6, 1, 0, 0, 0, 0, 0, 2, 6, 0, 0, 1, 1, 2, 0, 6, 6, 2, 5, 2, 0, 0, 6, 5, 5, 2, 0, 5, 6, 4, 3, 2, 2, 5, 5, 1, 1, 2, 6, 6, 1, 6, 6, 2, 0, 6, 6, 6, 6, 5, 6, 6, 6, 6, 0, 0, 5, 2, 5, 2, 6, 2, 5, 2, 1, 5, 4, 2, 4, 6, 5, 1, 5, 3, 2, 2, 6, 0, 2, 0, 2, 0, 4, 5, 6, 6, 6, 6, 6, 2, 2, 6, 2, 2, 6, 6, 6, 2, 5, 1, 0, 6, 1, 3, 6, 3, 2, 6, 2, 0, 6, 5, 6, 6, 2, 2, 6, 6, 5, 1, 2, 6, 1, 0, 6, 5, 1, 0, 2, 6, 2, 0, 3, 6, 6, 6, 0, 5, 2, 6, 2, 0, 6, 2, 5, 1, 0, 2, 2, 3, 2, 1, 2, 6, 6, 2, 6, 0, 2, 2, 2, 2, 2, 6, 5, 0, 6, 6, 6, 0, 0, 4, 2, 3, 6, 6, 5, 0, 3, 6, 6, 0, 0, 6, 3, 0, 6, 6, 2, 5, 6, 2, 6, 6, 6, 0, 1, 2, 2, 3, 3, 5, 6, 2, 2, 6, 5, 2, 2, 2, 6, 0, 6, 6, 6, 2, 2, 0, 2, 1, 0, 1, 2, 2, 6, 6, 5, 3, 1, 6, 5, 1, 6, 6, 5, 1, 1, 5, 2, 0, 2, 6, 0, 6, 2, 6, 1, 6, 5, 1, 6, 2, 6, 2, 6, 2, 2, 0, 6, 6, 2, 1, 4, 2, 6, 0, 6, 2, 1, 5, 0, 0, 2, 6, 0, 6, 2, 1, 1, 1, 6, 3, 6, 6, 0, 6, 0, 2, 2, 2, 6, 2, 2, 6, 6, 3, 5, 2, 6, 2, 6, 6, 2, 6, 2, 6, 0, 2, 2, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 0, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 3, 1, 1, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 5, 3, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 5, 1, 6, 6, 6, 6, 6, 5, 5, 3, 6, 6, 1, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 4, 0, 6, 6, 0, 6, 3, 6, 6, 5, 6, 6, 2, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 6, 6, 1, 6, 6, 6, 6, 6, 6, 4, 6, 1, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 1, 6, 6, 5, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 5, 6, 4, 3, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 3, 6, 6, 2, 6, 5, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 2, 3, 6, 3, 6, 6, 5, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 5, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 3, 6, 5, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 0, 1, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 4, 6, 6, 6, 6, 3, 6, 6, 6, 6, 0, 6, 6, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 1, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 2, 1, 6, 6, 6, 2, 3, 3, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 6, 5, 6, 1, 6, 6, 6, 1, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 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652, 653, 657, 658, 659, 663, 664, 668, 669, 670, 671, 672, 674, 675, 676, 677, 680, 681, 682, 685, 686, 687, 693, 694, 696, 697, 698, 699, 703, 705, 708, 710, 711, 712, 716, 717, 719, 720, 722, 723, 725, 729, 730, 733, 734, 735, 736, 737, 738, 739, 740, 741, 743, 744, 746, 747, 749, 750, 751, 752, 754, 756, 760, 761, 762, 764, 767, 768, 770, 771, 772, 773, 777, 781, 782, 784, 785, 786, 787, 788, 791, 792, 794, 797, 800, 801, 802, 804, 806, 807, 809, 812, 814, 816, 820, 821, 822, 823, 824, 826, 827, 828, 829, 831, 835, 836, 838, 839, 840, 841, 843, 844, 845, 847, 848, 852, 854, 855, 856, 857, 860, 861, 862, 863, 864, 867, 868, 870, 872, 873, 874, 875, 876, 878, 880, 882, 883, 887, 888, 890, 892, 893, 894, 896, 897, 899, 900, 901, 902, 907, 908, 909, 911, 912, 913, 916, 917, 918, 919, 921, 922, 923, 925, 928, 930, 931, 934, 937, 938, 939, 940, 942, 943, 945, 949, 950, 951, 952, 956, 957, 958, 959, 960, 962, 963, 965, 966, 968, 970, 972, 974, 975, 976, 978, 979, 983, 984, 985, 986, 989, 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1093, 96, 115, 143, 165, 192, 255, 301, 447, 531, 536, 542, 659, 732, 743, 755, 758, 763, 810, 941, 959, 981, 4, 26, 56, 111, 131, 138, 180, 291, 354, 370, 379, 388, 421, 439, 474, 479, 510, 520, 526, 541, 564, 573, 583, 586, 610, 623, 657, 665, 681, 717, 746, 788, 885, 901, 975, 1040, 1041, 1091, 1094, 15, 24, 77, 100, 147, 175, 258, 263, 484, 612, 641, 742, 784, 827, 928, 1015, 1060, 2, 22, 114, 132, 133, 189, 221, 234, 244, 302, 304, 311, 340, 391, 438, 446, 449, 489, 528, 539, 604, 607, 683, 700, 706, 740, 782, 817, 841, 919, 948, 950, 983, 1033, 1037, 1053, 1054, 1082, 0, 46, 67, 73, 183, 224, 237, 248, 256, 276, 289, 337, 353, 362, 553, 588, 592, 593, 616, 619, 710, 731, 747, 751, 769, 820, 822, 832, 850, 851, 892, 902, 921, 936, 947, 952, 958, 964, 986, 1069, 18, 57, 60, 105, 161, 164, 168, 191, 193, 200, 203, 216, 236, 252, 264, 299, 309, 321, 332, 333, 348, 374, 437, 465, 481, 498, 519, 534, 549, 554, 559, 567, 590, 640, 673, 687, 690, 699, 721, 739, 750, 787, 807, 811, 926, 933, 971, 1078, 1080, 1088, 6, 34, 35, 45, 65, 86, 108, 141, 148, 158, 162, 199, 271, 305, 315, 323, 343, 377, 385, 401, 450, 472, 480, 482, 501, 508, 525, 574, 600, 603, 633, 661, 670, 704, 714, 737, 753, 754, 768, 802, 829, 831, 877, 879, 886, 909, 937, 1008, 1019, 1020, 1042, 1056, 1089, 11, 20, 31, 47, 58, 62, 71, 92, 119, 145, 159, 179, 182, 218, 219, 220, 229, 249, 257, 270, 281, 290, 317, 320, 336, 349, 369, 381, 382, 408, 468, 477, 492, 511, 540, 544, 552, 585, 595, 631, 639, 656, 664, 677, 689, 702, 707, 774, 776, 790, 824, 838, 880, 890, 903, 906, 922, 932, 938, 949, 989, 993, 999, 1002, 1004, 1013, 1021, 1023, 1046, 1048, 1049, 1074, 1087, 13, 25, 32, 38, 82, 112, 117, 167, 196, 238, 251, 261, 272, 275, 278, 285, 324, 350, 363, 399, 415, 428, 443, 461, 473, 485, 532, 566, 578, 597, 613, 618, 650, 686, 688, 708, 726, 727, 756, 789, 793, 866, 875, 930, 934, 963, 965, 977, 980, 982, 994, 1050, 1051, 27, 48, 151, 240, 282, 292, 389, 409, 440, 453, 478, 523, 527, 591, 678, 724, 765, 805, 825, 864, 960, 973, 1027, 1036, 1038, 1058, 87, 103, 178, 211, 212, 283, 412, 460, 507, 515, 568, 572, 581, 644, 698, 762, 798, 803, 914, 157, 378, 819, 855, 898, 987, 3, 11, 17, 20, 28, 35, 40, 44, 51, 53, 57, 58, 60, 69, 81, 85, 90, 91, 96, 110, 119, 120, 125, 128, 129, 130, 134, 137, 141, 144, 145, 149, 152, 154, 156, 159, 169, 172, 177, 181, 184, 185, 193, 197, 202, 213, 215, 217, 219, 220, 222, 232, 242, 245, 246, 247, 255, 262, 266, 270, 281, 286, 287, 290, 293, 295, 300, 302, 303, 309, 310, 312, 314, 320, 323, 327, 338, 342, 345, 349, 351, 354, 358, 359, 364, 370, 376, 381, 386, 393, 401, 403, 411, 416, 436, 447, 448, 450, 451, 454, 465, 480, 481, 483, 488, 491, 492, 506, 511, 512, 522, 525, 534, 538, 544, 545, 555, 556, 557, 559, 561, 564, 569, 571, 577, 585, 595, 596, 598, 600, 602, 607, 616, 624, 630, 639, 664, 665, 668, 669, 672, 676, 692, 693, 695, 696, 697, 700, 701, 702, 713, 719, 720, 735, 736, 737, 752, 753, 764, 768, 771, 776, 777, 779, 781, 804, 806, 808, 810, 814, 816, 824, 829, 831, 851, 854, 859, 868, 883, 886, 892, 896, 899, 902, 903, 907, 908, 912, 916, 922, 924, 929, 935, 938, 940, 946, 948, 951, 954, 969, 970, 975, 976, 986, 989, 990, 993, 995, 996, 998, 1009, 1019, 1021, 1029, 1030, 1032, 1033, 1040, 1046, 1054, 1056, 1063, 1068, 1072, 1076, 1077, 1078, 1083, 1084, 1088, 1089, 1093, 1, 6, 13, 15, 21, 23, 34, 41, 42, 47, 49, 50, 54, 61, 62, 65, 67, 70, 71, 83, 89, 93, 94, 97, 104, 106, 108, 112, 113, 114, 115, 117, 121, 126, 127, 132, 136, 150, 163, 164, 167, 168, 170, 175, 176, 179, 180, 182, 190, 191, 196, 206, 208, 226, 238, 241, 248, 249, 251, 253, 261, 269, 274, 278, 280, 284, 285, 289, 296, 297, 298, 301, 305, 306, 317, 321, 322, 325, 330, 331, 336, 346, 350, 355, 357, 360, 374, 377, 382, 384, 392, 394, 397, 398, 404, 408, 415, 417, 418, 428, 432, 438, 443, 449, 452, 455, 466, 467, 468, 471, 473, 474, 475, 477, 479, 484, 486, 487, 496, 499, 500, 502, 513, 514, 518, 521, 523, 524, 526, 528, 529, 533, 541, 543, 546, 547, 573, 574, 580, 582, 597, 601, 608, 609, 611, 613, 618, 623, 626, 628, 631, 633, 635, 641, 643, 645, 649, 660, 666, 673, 679, 683, 685, 686, 687, 688, 689, 691, 706, 708, 716, 731, 734, 740, 742, 751, 759, 773, 774, 778, 780, 789, 791, 792, 793, 796, 799, 801, 813, 822, 836, 843, 845, 849, 850, 852, 860, 866, 867, 875, 876, 880, 881, 888, 890, 900, 904, 906, 913, 915, 918, 920, 926, 932, 942, 943, 947, 950, 955, 957, 958, 962, 965, 977, 978, 988, 992, 1001, 1003, 1006, 1012, 1014, 1018, 1022, 1025, 1028, 1034, 1050, 1051, 1052, 1059, 1062, 1069, 1070, 1074, 1075, 1079, 1082, 0, 2, 4, 8, 9, 10, 12, 14, 18, 22, 29, 30, 31, 32, 39, 43, 55, 59, 76, 77, 82, 105, 107, 122, 123, 135, 138, 148, 151, 153, 155, 160, 161, 165, 173, 174, 183, 189, 194, 201, 203, 207, 209, 210, 216, 218, 227, 235, 252, 256, 258, 259, 264, 265, 267, 268, 271, 279, 291, 304, 307, 326, 333, 334, 335, 337, 343, 348, 352, 361, 367, 371, 388, 389, 390, 400, 402, 406, 407, 409, 414, 420, 422, 423, 424, 427, 430, 431, 433, 434, 441, 442, 444, 456, 457, 458, 463, 469, 472, 476, 490, 493, 497, 501, 508, 520, 527, 530, 531, 535, 536, 537, 548, 550, 551, 554, 558, 562, 563, 566, 570, 575, 578, 579, 583, 586, 589, 590, 592, 594, 599, 604, 617, 619, 620, 621, 629, 638, 640, 646, 647, 650, 653, 654, 656, 657, 663, 667, 674, 682, 690, 699, 709, 710, 712, 717, 718, 723, 732, 741, 744, 745, 758, 765, 767, 784, 788, 794, 797, 800, 802, 805, 811, 817, 820, 825, 826, 830, 834, 837, 838, 839, 840, 841, 842, 844, 848, 856, 864, 872, 885, 887, 893, 895, 919, 921, 923, 925, 927, 934, 953, 961, 967, 973, 980, 982, 983, 985, 1002, 1005, 1010, 1020, 1023, 1024, 1027, 1037, 1041, 1043, 1047, 1055, 1061, 1067, 1080, 1091, 1092, 5, 7, 19, 25, 36, 37, 46, 48, 56, 64, 72, 75, 79, 80, 84, 86, 87, 88, 92, 95, 102, 116, 124, 131, 133, 139, 143, 146, 166, 178, 186, 187, 188, 192, 195, 198, 199, 204, 205, 212, 221, 223, 224, 225, 229, 231, 243, 257, 260, 273, 275, 282, 283, 292, 294, 299, 308, 311, 313, 315, 316, 318, 319, 328, 329, 332, 339, 341, 347, 356, 362, 363, 365, 366, 373, 375, 379, 383, 387, 391, 396, 399, 405, 410, 421, 425, 426, 429, 435, 437, 439, 440, 445, 453, 459, 460, 461, 462, 464, 478, 482, 485, 489, 494, 495, 498, 504, 505, 507, 509, 510, 515, 516, 517, 519, 540, 542, 549, 552, 553, 568, 572, 576, 581, 584, 587, 588, 591, 593, 605, 606, 610, 612, 622, 632, 636, 637, 642, 644, 651, 652, 659, 661, 662, 670, 671, 675, 677, 678, 681, 694, 707, 715, 722, 724, 725, 726, 727, 728, 729, 733, 738, 739, 743, 746, 747, 749, 754, 755, 756, 760, 761, 763, 770, 775, 782, 783, 785, 790, 798, 803, 807, 809, 821, 823, 827, 828, 833, 846, 847, 853, 857, 858, 863, 865, 870, 873, 874, 877, 879, 882, 884, 889, 891, 894, 897, 901, 909, 911, 914, 917, 928, 930, 931, 933, 936, 937, 941, 944, 945, 952, 956, 963, 966, 968, 971, 974, 979, 981, 984, 991, 994, 997, 1000, 1004, 1007, 1008, 1013, 1015, 1016, 1017, 1031, 1035, 1036, 1038, 1039, 1042, 1044, 1045, 1048, 1057, 1058, 1064, 1066, 1071, 1073, 1087, 1090, 16, 24, 26, 27, 33, 38, 45, 52, 63, 66, 68, 73, 74, 78, 98, 99, 100, 101, 103, 109, 111, 118, 140, 142, 147, 157, 158, 162, 171, 200, 211, 214, 228, 230, 233, 234, 236, 237, 239, 240, 244, 250, 254, 263, 272, 276, 277, 288, 324, 340, 344, 353, 368, 369, 372, 378, 380, 385, 395, 412, 413, 419, 446, 470, 503, 532, 539, 560, 565, 567, 603, 614, 615, 625, 627, 634, 648, 655, 658, 680, 684, 698, 703, 704, 705, 711, 714, 721, 730, 748, 750, 757, 762, 766, 769, 772, 786, 787, 795, 812, 815, 818, 819, 832, 835, 855, 861, 862, 869, 871, 878, 898, 905, 910, 939, 949, 959, 960, 964, 972, 987, 999, 1011, 1026, 1049, 1053, 1060, 1065, 1081, 1085, 1086, 1094, NA, NA, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, log(vSalePrice) ~ vAlley + vBldgType + vBsmtCond + vBsmtExposure + , vBsmtFinType1 + vBsmtFinType2 + vBsmtQual + vCentralAir + , vCondition1 + vCondition2 + vElectrical + vExterCond + vExterior1st + , vExterior2nd + vExterQual + vFence + vFireplaceQu + vFoundation + , vFunctional + vGarageCond + vGarageFinish + vGarageQual + , vGarageType + vHeating + vHeatingQC + vHouseStyle + vKitchenQual + , vLandContour + vLandSlope + vLotConfig + vLotShape + vMasVnrType + , vMiscFeature + vMSSubClass + vMSZoning + vNeighborhood + , vPavedDrive + vPoolQC + vRoofMatl + vRoofStyle + vSaleCondition + , vSaleType + vStreet + vId1 + v1stFlrSF + v2ndFlrSF + v3SsnPorch + , vBedroomAbvGr + vBsmtFinSF1 + vBsmtFinSF2 + vBsmtFullBath + , vBsmtHalfBath + vBsmtUnfSF + vEnclosedPorch + vFireplaces + , vFullBath + vGarageArea + vGarageCars + vGarageYrBlt + vGrLivArea + , vHalfBath + vKitchenAbvGr + vLotArea + vLotFrontage + vLowQualFinSF + , vMasVnrArea + vMiscVal + vMoSold + vOpenPorchSF + vOverallCond + , vOverallQual + vPoolArea + vScreenPorch + vTotalBsmtSF + , vTotRmsAbvGrd + vWoodDeckSF + vYearBuilt + vYearRemodAdd + , vYrSold, 0, gbm(formula = log(vSalePrice) ~ ., distribution = "gaussian", , data = entrena, n.trees = 500, interaction.depth = depth, , shrinkage = shrinkage, bag.fraction = bag.fraction, train.fraction = 0.75), model.frame(formula = log(vSalePrice) ~ ., data = entrena, drop.unused.levels = TRUE, , na.action = function (object, ...) , object)
## eval
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0.131515876145983, 0.131669298643345, 0.131641540977615, 0.131752649152988, 0.131564897472806, 0.131445628644333, 0.131339127955174, 0.131503169286209, 0.131669253705342, 0.131350165900902, 0.131562784699126, 0.1316512527382, 0.131881909137094, 0.131870353396694, 0.131812679970278, 0.131942575074169, 0.131627941379097, 0.131776401379543, 0.131724662078687, 0.131752242440733, 0.131748126198284, 0.131745639669841, 0.131700144436395, 0.131556970192177, 0.131830340381816, 0.131788769919748, 0.131787565860162, 0.1317493051049, 0.131868263848307, 0.131647881859615, 0.131717192893815, 0.131818614561226, 0.131843930438804, 0.131970276615398, 0.132243137001134, 0.131971996706686, 0.132160181657825, 0.131993694012931, 0.131993000237088, 0.13188605626294graf_eval <- modelos_dat %>% select(shrinkage, bag.fraction, eval) %>% unnest
head(graf_eval)## shrinkage bag.fraction n_arbol tipo valor
## 1 0.01 0.1 1 entrena 0.4016655
## 2 0.01 0.1 2 entrena 0.3991252
## 3 0.01 0.1 3 entrena 0.3964301
## 4 0.01 0.1 4 entrena 0.3942135
## 5 0.01 0.1 5 entrena 0.3914665
## 6 0.01 0.1 6 entrena 0.3891097ggplot(filter(graf_eval, tipo =='valida'), aes(x = n_arbol, y= valor, colour=factor(bag.fraction), group =
bag.fraction)) + geom_line() +
facet_wrap(~shrinkage)
Bag fraction demasiado chico no funciona bien, especialmente si la tasa de aprendizaje es alta (¿Por qué?). Filtremos para ver con detalle el resto de los datos:
ggplot(filter(graf_eval, tipo =='valida', bag.fraction>0.1), aes(x = n_arbol, y= valor, colour=factor(bag.fraction), group =
bag.fraction)) + geom_line() +
facet_wrap(~shrinkage) + scale_y_log10()
Y parece ser que para este número de iteraciones, una tasa de aprendizaje de 0.1 junto con un bag fraction de 0.5 funciona bien:
graf_eval %>% filter(tipo=='valida') %>%
group_by(shrinkage, bag.fraction) %>%
summarise(valor = min(valor)) %>%
arrange(valor)## # A tibble: 16 x 3
## # Groups: shrinkage [4]
## shrinkage bag.fraction valor
## <dbl> <dbl> <dbl>
## 1 0.10 0.50 0.1246740
## 2 0.25 0.50 0.1283885
## 3 0.10 1.00 0.1305941
## 4 0.10 0.25 0.1310472
## 5 0.01 0.25 0.1311681
## 6 0.10 0.10 0.1320537
## 7 0.25 0.25 0.1333946
## 8 0.25 1.00 0.1349612
## 9 0.01 0.50 0.1366676
## 10 0.01 0.10 0.1367777
## 11 0.01 1.00 0.1407490
## 12 0.50 1.00 0.1480422
## 13 0.25 0.10 0.1560010
## 14 0.50 0.50 0.1587105
## 15 0.50 0.25 0.1676023
## 16 0.50 0.10 0.195596312.3.3 Número de árboles M
Se monitorea el error sobre una muestra de validación cuando agregamos cada árboles. Escogemos el número de árboles de manera que minimize el error de validación. Demasiados árboles pueden producir sobreajuste. Ver el ejemplo de arriba.
12.3.4 Tamaño de árboles
Los árboles se construyen de tamaño fijo \(J\), donde \(J\) es el número de cortes. Usualmente \(J=1,2,\ldots, 10\), y es un parámetro que hay que elegir. \(J\) más grande permite interacciones de orden más alto entre las variables de entrada. Se intenta con varias \(J\) y \(M\) para minimizar el error de vaidación.
12.3.5 Controlar número de casos decidir si hacemos cortes
Igual que en bosques aleatorios, podemos establecer mínimos de muestra en nodos terminales, o mínimo de casos necesarios para hacer un corte.
Ejemplo
modelos_dat <- list(bag.fraction = c( 0.25, 0.5, 1),
shrinkage = c(0.01, 0.1, 0.25, 0.5),
depth = c(1,5,10,12)) %>% expand.grid
modelos_dat <- modelos_dat %>%
mutate(modelo = pmap(., boost)) %>%
mutate(eval = map(modelo, eval_modelo))
graf_eval <- modelos_dat %>% select(shrinkage, bag.fraction, depth, eval) %>% unnest
ggplot(filter(graf_eval, tipo =='valida'), aes(x = n_arbol, y= valor, colour=factor(bag.fraction), group =
bag.fraction)) + geom_line() +
facet_grid(depth~shrinkage) + scale_y_log10()
Bishop, Christopher M. 2006. Pattern Recognition and Machine Learning (Information Science and Statistics). Secaucus, NJ, USA: Springer-Verlag New York, Inc.
Goodfellow, Ian, Yoshua Bengio, and Aaron Courville. 2016. Deep Learning. MIT Press.
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2017. The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc. http://web.stanford.edu/~hastie/ElemStatLearn/.
James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2014. An Introduction to Statistical Learning: With Applications in R. Springer Publishing Company, Incorporated. http://www-bcf.usc.edu/~gareth/ISL/.
Ng, Andrew. 2017. “Machine Learning.” https://www.coursera.org/learn/machine-learning.
Srivastava, Nitish, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. 2014. “Dropout: A Simple Way to Prevent Neural Networks from Overfitting.” J. Mach. Learn. Res. 15 (1). JMLR.org: 1929–58. http://dl.acm.org/citation.cfm?id=2627435.2670313.
References
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2017. The Elements of Statistical Learning. Springer Series in Statistics. Springer New York Inc. http://web.stanford.edu/~hastie/ElemStatLearn/.